749:
724:
3195:
741:
43:
88:
6174:
5514:), except for that a full circle doesn't equal 360 degree, 6.2831... rad or 400 gon, but 1 turn. (I found it to be really convenient in engineering/programming, where you often have to convert to/from other unit representations But I think it can also be useful for educational purposes. ) Having the angle of a full circle normalized to 1 allows for easier
2906:
463:) and corresponding to one turn, for greater conceptual simplicity when stating angles in radians. This proposal did not initially gain widespread acceptance in the mathematical community, but the constant has become more widespread, having been added to several major programming languages and calculators.
4696:
The following table documents various programming languages that have implemented the circle constant for converting between turns and radians. All of the languages below support the name "Tau" in some casing, but
Processing also supports "TWO_PI" and Raku also supports the symbol "τ" for accessing
3010:
5977:
2791:
5372:"Richtlinie 2009/3/EG des Europäischen Parlaments und des Rates vom 11. März 2009 zur Änderung der Richtlinie 80/181/EWG des Rates zur Angleichung der Rechtsvorschriften der Mitgliedstaaten über die Einheiten im Messwesen (Text von Bedeutung für den EWR)"
6546:[from which it is clear that the point B is pushed by a given distance from its natural position, and it will reach the maximum distance after the elapsed time t=π/m, π denoting an angle of 180°, which becomes cos(mt)=- 1 & B b=2α.]
2429:
2331:
2629:
2555:
727:
An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to a full turn, or approximately 6.28 radians, which is expressed here using the Greek letter
2773:
2707:
6169:{\displaystyle {\overline {{\tfrac {16}{5}}-{\tfrac {4}{239}}}}-{\tfrac {1}{3}}{\overline {{\tfrac {16}{5^{3}}}-{\tfrac {4}{239^{3}}}}}+{\tfrac {1}{5}}{\overline {{\tfrac {16}{5^{5}}}-{\tfrac {4}{239^{5}}}}}-,\,\&c.=}
2912:
1873:
1821:
4491:
6744:; Chen, Hongyu; Aylward, Graeme; Jorritsma, Megan; Mann, Christina; Defaz Poveda, Diego David; Pierce, Cayden; Lam, Derek; Stairs, Jeremy; Hermandez, Jesse; Li, Qiushi; Xiang, Yi Xin; Kanaan, Georges (June 2019).
1480:
1049:, 𐤈 or ט, and it has been observed that the older version of the symbol, which means wheel, resembles a wheel with four spokes. It has also been proposed to use the wheel symbol, teth, to represent the value 2
1443:
1716:
2193:
2043:
5347:"Richtlinie 80/181/EWG - Richtlinie des Rates vom 20. Dezember 1979 zur Angleichung der Rechtsvorschriften der Mitgliedstaaten über die Einheiten im Meßwesen und zur Aufhebung der Richtlinie 71/354/EWG"
4569:
4406:
6544:
unde constat punctum B per datum tantum spatium de loco fuo naturali depelli, ad quam maximam distantiam pertinget, elapso tempore t=π/m denotante π angulum 180°, quo fit cos(mt)=- 1 & B b=2α.
3180:
3146:
3090:
3056:
2119:
1966:
2901:{\displaystyle e^{{\color {orangered}2\pi }i{\frac {k}{n}}}=\cos {\frac {{\color {orangered}2}k{\color {orangered}\pi }}{n}}+i\sin {\frac {{\color {orangered}2}k{\color {orangered}\pi }}{n}}}
1665:
1594:
1560:
1053:, and more recently a connection has been made among other ancient cultures on the existence of a wheel, sun, circle, or disk symbol—i.e. other variations of teth—as representation for 2
953:, which amounts to the number of radians in half a turn, in order to make mathematics simpler and more intuitive. His proposal used a "π with three legs" symbol to denote the constant (
988:
5510:
I'd like to see a TURN mode being implemented as well. TURN mode works exactly like DEG, RAD and GRAD (including having a full set of angle unit conversion functions like on the
4993:
6438:
Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et
Ferdinand Rudio
1032:
2337:
2236:
2450:
2561:
2484:
461:
426:
391:
792:
5375:
5792:
2713:
2644:
2470:
5350:
5468:
5768:
7503:
6902:
644:
While percentage protractors have existed since 1922, the terms centiturns, milliturns and microturns were introduced much later by the
British astronomer
5599:
7391:
5550:
5265:
3005:{\displaystyle e^{{\color {orangered}\tau }i{\frac {k}{n}}}=\cos {\frac {k{\color {orangered}\tau }}{n}}+i\sin {\frac {k{\color {orangered}\tau }}{n}}}
6870:
6960:
4434:, resulting from a ratio of angular displacement. It can be negative and also greater than 1 in modulus. The relationship between quantity rotation,
1078:. He offered several reasons for the choice of constant, primarily that it allows fractions of a turn to be expressed more directly: for instance, a
6411:
6467:
5735:
5187:
4766:
7492:
7435:
7131:
6893:"Let's Use Tau--It's Easier Than Pi - A growing movement argues that killing pi would make mathematics simpler, easier and even more beautiful"
1827:
1772:
6191:(among others for the same purpose, and drawn from the same Principle) I receiv'd from the Excellent Analyst, and my much Esteem'd Friend Mr.
5050:"Measurement units of quantities of dimension one are numbers. In some cases, these measurement units are given special names, e.g. radian..."
4444:
1207:(which Hartl also calls "Euler's identity") is more fundamental and meaningful. He also claims that the formula for circular area in terms of
6301:
7335:
522:
5408:
6235:
1449:
6277:
5948:
5944:
5938:
5498:
1412:
5438:
512:
6328:. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (in French). Vol. 19 (published 1886). p. 139.
5223:
4362:
is the number (not necessarily an integer) of revolutions, for example, of a rotating body about a given axis. Its value is given by:
7409:
5130:
5126:
692: turn. The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single
1671:
1260:
Initially, this proposal did not receive significant acceptance by the mathematical and scientific communities. However, the use of
6674:"Trig rerigged. Trigonometry reconsidered. Measuring angles in 'unit meter around' and using the unit radius functions Xur and Yur"
5733:
Croxton, Frederick E. (1922). "A Percentage
Protractor - Designed for Use in the Construction of Circle Charts or "Pie Diagrams"".
2124:
1971:
4784:
5906:
5023:
The angular unit terms "cycles" and "revolutions" are also used, ambiguously, as shorter versions of the related frequency units.
914:, sometimes for 3.14... and other times for 6.28..., became widespread, with the definition varying as late as 1761; afterward,
6673:
5848:
5261:
Handbuch SI-Einheiten: Definition, Realisierung, Bewahrung und
Weitergabe der SI-Einheiten, Grundlagen der Präzisionsmeßtechnik
6446:
4527:
4368:
7472:
5683:
The
Science of Measurement: A Historical Survey (The World of Measurements: Masterpieces, Mysteries and Muddles of Metrology)
5095:
97:
about the center point starting from the right, where a complete rotation corresponds to an angle of rotation of 1 turn.
5918:
5852:
5702:
5643:
5593:
5544:
5323:
5277:
7019:
6931:
893:
3152:
3115:
7207:
7073:
6990:
6734:
5371:
4802:
4334:
3062:
3025:
2050:
1897:
467:
6793:
6622:
1630:
1300:
52:
5346:
949:
In 2001, Robert Palais proposed using the number of radians in a turn as the fundamental circle constant instead of
7044:
5460:
1566:
1529:
470:, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a
7102:
5777:
17:
7152:
1354:
7591:
6892:
6593:
5812:
4743:
4717:
7360:
5580:
5163:
5041:"The special name revolution, symbol r, for this unit is widely used in specifications on rotating machines."
956:
7586:
5934:
5004:
4855:
4761:
4424:
1292:
863:
795:
562:
support the unit symbol "tr" for turns since 2011 and 2013, respectively. Support for "tr" was also added to
7246:
7170:
6858:
5883:
5531:
2477:
2229:
31:
6952:
997:
proposed the idea of defining a constant as the ratio of circumference to radius, a proposal supported by
6408:
5515:
4893:
4873:
4797:
2637:
1320:
1308:
1296:
4911:
4815:
4320:
1304:
655:
5490:
5197:
7459:
6537:
5694:
5430:
5404:
4431:
543:
7123:
4898:
5686:
4682:: rotation and angle, respectively. "Cycle" is also mentioned in ISO 80000-3, in the definition of
2424:{\displaystyle f(a)={\frac {1}{{\color {orangered}\tau }i}}\oint _{\gamma }{\frac {f(z)}{z-a}}\,dz}
2326:{\displaystyle f(a)={\frac {1}{{\color {orangered}2\pi }i}}\oint _{\gamma }{\frac {f(z)}{z-a}}\,dz}
630:
4916:
4779:
1312:
6298:
6212:
4748:
4675:
4654:
4412:
3100:
1008:
7328:
5910:
4730:
4502:
4956:
4726:
4596:
2624:{\displaystyle \varphi (x)={\frac {1}{\sqrt {\color {orangered}\tau }}}e^{-{\frac {x^{2}}{2}}}}
2550:{\displaystyle \varphi (x)={\frac {1}{\sqrt {\color {orangered}2\pi }}}e^{-{\frac {x^{2}}{2}}}}
471:
339:
7542:
7447:
6482:
6385:
6323:
6243:
5763:
5678:
5396:
5259:
5081:
7282:
Harremoës, Peter (2017). "Bounds on tail probabilities for negative binomial distributions".
6741:
6708:; Janzen, Ryan E.; Ali, Mir Adnan; Scourboutakos, Pete; Guleria, Nitin (22–24 October 2014).
6705:
6258:
2435:
659:
6828:
4510:
1881:
443:
411:
373:
344:
7489:"The NIST Guide for the Use of the International System of Units, Special Publication 811"
5901:
The Words of
Mathematics: An Etymological Dictionary of Mathematical Terms Used in English
5117:
2768:{\displaystyle n!\sim {\sqrt {{\color {orangered}\tau }n}}\left({\frac {n}{e}}\right)^{n}}
2702:{\displaystyle n!\sim {\sqrt {{\color {orangered}2\pi }n}}\left({\frac {n}{e}}\right)^{n}}
858:
on its own with its present meaning (of perimeter divided by diameter) was in 1706 by the
777:
8:
7601:
6897:
6710:"Integral Kinematics (Time-Integrals of Distance, Energy, etc.) and Integral Kinesiology"
5844:
5690:
5229:
4966:
4614:
1191:
696:. Other measures of angle used in computing may be based on dividing one whole turn into
6832:
6484:
Cursus
Mathematicus: Elementorum Analyseos Infinitorum Elementorum Analyseos Infinitorvm
5797:. History of the Smithsonian Satellite-tracking Program. Cambridge, Massachusetts, USA:
854:(delta over pi) for the ratio of the diameter to perimeter. The first use of the symbol
7383:
7309:
7291:
7011:
6786:
6761:
6717:
6614:
6461:
6359:
6206:
s Number, or that in Art. 64.38. may be Examin'd with all desireable Ease and
Dispatch.
6199:
5899:
4860:
4671:
4670:
The superseded version ISO 80000-3:2006 defined "revolution" as a special name for the
2455:
1316:
998:
910:
for one-fourth of the circumference of a unit circle, or 1.57... . Usage of the letter
649:
6840:
5397:"Art. 15 Einheiten in Form von nichtdezimalen Vielfachen oder Teilen von SI-Einheiten"
794:
was not originally fixed to the ratio of the circumference and the diameter. In 1697,
355:
of curves. Subdivisions of a turn include the half-turn and quarter-turn, spanning a
343:(rpm). The angular unit of the turn is useful in connection with, among other things,
7468:
7387:
7313:
6765:
6745:
6709:
6618:
5914:
5708:
5698:
5655:
5647:
5589:
5540:
5319:
5273:
5234:
5091:
5059:"3-14) period duration, period: duration (item 3‑9) of one cycle of a periodic event"
4951:
4590:
4575:
4348:
3108:
1330:
It has also been used in at least one mathematical research article, authored by the
333:
61:
57:
6680:
6508:
600:
7488:
7375:
7301:
6854:
6836:
6753:
6721:
6606:
6436:
6351:
5748:
5744:
5311:
4999:
4961:
4945:
4882:
4684:
4679:
1623:
1155:
994:
829:
4678:, these two specially named dimensionless units are applicable for non-comparable
4674:"one", which also received other special names, such as the radian. Despite their
4419:
The above definition is part of the ISQ, formalized in the international standard
7379:
6602:
6542:(in Latin). sumtibus Ambr. Haude & Jo. Carol. Speneri, bibliop. p. 200.
6415:
6305:
5877:
5307:
5303:
Das Vieweg
Einheiten-Lexikon: Formeln und Begriffe aus Physik, Chemie und Technik
5301:
5269:
5192:
3018:
1721:
364:
271:
268:
4878:
718:
7596:
7226:
6647:
6533:
6342:
Cajori, Florian (1913). "History of the Exponential and Logarithmic Concepts".
5798:
4842:
3275:
3249:
870:
869:
The first known usage of a single letter to denote the 6.28... constant was in
748:
356:
352:
292:
221:
7189:
6923:
6558:
6442:
6393:
6329:
6273:
5315:
5188:"Life of pi in no danger – Experts cold-shoulder campaign to replace with tau"
7580:
7305:
6819:
5873:
5636:
5238:
4987:
4325:
4291:
number of revolutions, number of cycles, number of turns, number of rotations
3199:
2781:
1061:
825:
764:
668:
527:
433:
405:
7065:
6982:
6757:
6585:
4838:
7264:
5659:
1599:
1271:
300:
7517:
7431:
6698:
4820:
4579:
328:
6193:
4970:
4936:
4420:
3203:
1868:{\displaystyle A={\frac {n}{2}}\sin {\frac {\color {orangered}\tau }{n}}}
1816:{\displaystyle A={\frac {n}{2}}\sin {\frac {\color {orangered}2\pi }{n}}}
1136: rad. As for the choice of notation, he offered two reasons. First,
1002:
899:
360:
348:
264:
186:
112:
7467:(9th ed.), International Bureau of Weights and Measures, Dec 2022,
7040:
5616:
5567:
4486:{\displaystyle N={\frac {\varphi }{\text{tr}}}=\{\varphi \}_{\text{tr}}}
6610:
6392:(in Latin). Vol. 1. Academiae scientiarum Petropoli. p. 113.
6363:
5969:, which may very much facilitate the Practice; as for instance, in the
5685:. Dover Books on Mathematics (corrected reprint of original ed.).
5631:
4833:
4662:
4514:
1045:. The Greek letter theta derives from the Phoenician and Hebrew letter
645:
638:
634:
367:
can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.
7153:"Constants @GDScript - Godot Engine (stable) documentation in English"
7094:
5614:
5565:
1178:
gives many examples of formulas that are asserted to be clearer where
6817:
Aron, Jacob (2011-01-08). "Michael Hartl: It's time to kill off pi".
5087:
4981:
1324:
1174:, whose association with the circle constant is unavoidable. Hartl's
1037:
The same year, Thomas Colignatus proposed the uppercase Greek letter
887:
821:
723:
662:, which implicitly have an angular separation of 1/32 turn. The
6355:
5823:
7569:
7296:
5588:. 0.12 (draft ed.). pp. iii, 54, 97, 128, 144, 193, 195.
4313:
1475:{\displaystyle {\color {orangered}{\frac {\tau }{4}}}{\text{ rad}}}
1254:
898:
though defined as half the circumference of a circle of radius 1—a
616:
575:
571:
559:
555:
94:
5159:
1438:{\displaystyle {\color {orangered}{\frac {\pi }{2}}}{\text{ rad}}}
902:—rather than the ratio of circumference to diameter. Elsewhere in
484:
of a given angle and a full turn. It is represented by the symbol
87:
4308:
3280:
3253:
1761:
658:
are also used. Sailors have traditionally divided a turn into 32
583:
579:
539:
296:
237:
7432:"ISO 80000-3:2019 Quantities and units — Part 3: Space and time"
5712:
5651:
707:
7231:
6390:
Mechanica sive motus scientia analytice exposita. (cum tabulis)
5511:
4994:
Divine Proportions: Rational Trigonometry to Universal Geometry
3270:
3245:
3207:
3194:
1288:
768:
591:
567:
563:
437:
288:
275:
152:
5820:
Manual & Technical Specifications - ooPIC Compiler Ver 6.0
5224:"For Math Fans, Nothing Can Spoil Pi Day—Except Maybe Tau Day"
4500:
is the numerical value of the angle 𝜑 in units of turns (see
1711:{\displaystyle A={\color {orangered}{\frac {1}{2}}\tau }r^{2}}
7543:"ISO 80000-1:2009(en) Quantities and units — Part 1: General"
5817:
5119:
Units & Symbols for Electrical & Electronic Engineers
4941:
4584:
2188:{\displaystyle S_{n}(r)={\color {orangered}\tau }rV_{n-1}(r)}
2038:{\displaystyle S_{n}(r)={\color {orangered}2\pi }rV_{n-1}(r)}
1338:
The following table shows how various identities appear when
1038:
859:
740:
626:
481:
6334:
Car, soit π la circonference d'un cercle, dout le rayon est
30:"360 degrees" and "360°" redirect here. For other uses, see
7413:
4721:
1046:
693:
7190:"JDK-8283136: Add constant for tau to Math and StrictMath"
6704:
6266:
Commentarii Academiae Scientiarum Imperialis Petropolitana
6866:
6750:
The 5th ACM Workshop on Wearable Systems and Applications
1065:
729:
515:(March 1974) proposed the unit symbol "pla" (from Latin:
429:
6740:
5389:
4564:{\displaystyle n={\frac {\mathrm {d} N}{\mathrm {d} t}}}
4401:{\displaystyle N={\frac {\varphi }{2\pi {\text{ rad}}}}}
752:
A comparison of angles expressed in degrees and radians.
6746:"Eye Itself as a Camera: Sensors, Integrity, and Trust"
6539:
Nova theoria lucis et colorum. Opuscula varii argumenti
6312:
is taken for the ratio of the radius to the periphery "
281:
6425:
denote the ratio of the diameter to the circumference"
6123:
6101:
6086:
6058:
6036:
6021:
6000:
5985:
744:
Some special angles in radians, stated in terms of 𝜏.
6441:(in Latin). Lipsae: B.G. Teubneri. pp. 133–134.
5980:
5769:
Astronomische Mitteilungen der Urania-Sternwarte Wien
4530:
4447:
4371:
3155:
3118:
3065:
3028:
2915:
2794:
2716:
2647:
2564:
2487:
2458:
2438:
2340:
2239:
2127:
2053:
1974:
1900:
1830:
1775:
1674:
1633:
1569:
1532:
1452:
1415:
1011:
959:
780:
446:
414:
376:
5539:. 0.12 (draft ed.). pp. 72, 118–119, 311.
1158:
648:
in 1962. Some measurement devices for artillery and
625:
milliturns, with each milliturn corresponding to an
7512:
7510:
7227:"Add Math.Tau Pull Request #37517 · dotnet/Runtime"
6372:
be the circumference (!) of a circle of unit radius
5266:
Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
828:) divided by its radius. However, earlier in 1647,
594:
as well, but the calculator instead implements "MUL
7487:Thompson, Ambler; Taylor, Barry N. (2020-03-04) .
7426:
7424:
7422:
7163:
6168:
5898:
5635:
5222:
4563:
4485:
4400:
3175:{\displaystyle \omega ={\color {orangered}\tau }f}
3174:
3141:{\displaystyle \omega ={\color {orangered}2\pi }f}
3140:
3084:
3050:
3004:
2900:
2767:
2701:
2623:
2549:
2464:
2444:
2423:
2325:
2187:
2113:
2037:
1960:
1867:
1815:
1710:
1659:
1588:
1554:
1474:
1437:
1026:
982:
786:
455:
420:
385:
3085:{\displaystyle h={\color {orangered}\tau }\hbar }
3051:{\displaystyle h={\color {orangered}2\pi }\hbar }
2114:{\displaystyle V_{n}(r)={\frac {r}{n}}S_{n-1}(r)}
1961:{\displaystyle V_{n}(r)={\frac {r}{n}}S_{n-1}(r)}
967:
966:
965:
963:
921:Several people have independently proposed using
7578:
7507:
6884:
5890:
5822:. Savage Innovations, LLC. 2007 . Archived from
5182:
5180:
763:(approximately 6.28) is the ratio of a circle's
27:Unit of plane angle where a full circle equals 1
7419:
5837:
5736:Journal of the American Statistical Association
5216:
5214:
5073:
1660:{\displaystyle A={\color {orangered}\pi }r^{2}}
7493:National Institute of Standards and Technology
7480:
7436:International Organization for Standardization
7401:
7320:
7275:
6579:
6577:
6493:notet peripheriam circuli, cuius diameter eſt
6322:Euler, Leonhard (1747). Henry, Charles (ed.).
5755:
4517:of rotation with respect to time), denoted by
1274:began accepting answers expressed in terms of
5866:
5813:"ooPIC Programmer's Guide - Chapter 15: URCP"
5672:
5670:
5626:
5624:
5572:
5523:
5461:"Chapter 3: Units - Available Units - Angles"
5177:
4430:Rotation count or number of revolutions is a
1291:and in several programming languages such as
918:was standardized as being equal to 3.14... .
503:There are several unit symbols for the turn.
7452:
6563:(YouTube video). Information shown at 18:35
6259:"Tentamen explicationis phaenomenorum aeris"
5953:There are various other ways of finding the
5726:
5452:
5422:
5293:
5258:German, Sigmar; Drath, Peter (2013-03-13) .
5211:
5153:
5151:
4474:
4467:
1589:{\displaystyle C={\color {orangered}\tau }r}
1555:{\displaystyle C={\color {orangered}2\pi }r}
1287:is made available in the Google calculator,
1190:. For example, Hartl asserts that replacing
708:Proposals for a single letter to represent 2
637:divided in centiturns is normally called a "
533:
7535:
7352:
7239:
7171:"Get TAU - Unreal Engine 5.2 Documentation"
6974:
6916:
6890:
6847:
6574:
6466:: CS1 maint: numeric names: authors list (
6227:
5973:, the Diameter is to Circumference as 1 to
5896:
5805:
5518:to/from a whole bunch of other angle units
5306:(in German) (1 ed.). Vieweg, reprint:
5257:
5079:
4691:
4574:The SI unit of rotational frequency is the
4438:, and unit turns, tr, can be expressed as:
621:A turn can be divided in 100 centiturns or
516:
7058:
7004:
6891:Bartholomew, Randyn Charles (2014-06-25).
6778:
6557:sudgylacmoe; Hartl, Michael (2023-06-28).
6526:
6292:Sumatur pro ratione radii ad peripheriem,
5784:
5766:(ed.). "Bestimmung von Satellitenbahnen".
5667:
5621:
5251:
4509:In the ISQ/SI, rotation is used to derive
964:
86:
7326:
7295:
7281:
7257:
7200:
6810:
6672:Cool, Thomas "Colignatus" (2008-07-18) .
6665:
6153:
5849:"Angles, integers, and modulo arithmetic"
5761:
5482:
5148:
5127:Institution of Engineering and Technology
2414:
2316:
1266:has become more widespread. For example:
771:, and the number of radians in one turn.
7145:
5872:
5299:
5220:
3193:
983:{\displaystyle \pi \!\;\!\!\!\pi =2\pi }
747:
739:
722:
6980:
5907:The Mathematical Association of America
5732:
5458:
5428:
5364:
5339:
5110:
4973:counterpart of the turn, equivalent to
3163:
3126:
3073:
3036:
2990:
2959:
2922:
2886:
2876:
2848:
2838:
2801:
2729:
2660:
2586:
2509:
2363:
2262:
2151:
1998:
1855:
1800:
1682:
1641:
1577:
1540:
1454:
1417:
629:of 0.36°, which can also be written as
14:
7579:
7358:
7218:
6945:
6853:
6645:
6583:
6560:The Tau Manifesto - With Michael Hartl
6480:
6341:
6233:
5843:
5459:Lapilli, Claudio Daniel (2018-10-25).
5429:Lapilli, Claudio Daniel (2016-05-11).
875:Essay Explaining the Properties of Air
7033:
6784:
6716:. Toronto, Ontario, Canada: 627–629.
6532:
6434:
6383:
6325:Lettres inédites d'Euler à d'Alembert
6321:
6256:
6210:
5933:
5927:
5801:/ Howard A. Doyle Publishing Company.
5790:
5676:
5644:Macdonald & Co. (Publishers) Ltd.
5630:
5578:
5529:
5282:. 978-3-528-08441-7, 978-3-32283606-9
5157:
4423:(Space and time), and adopted in the
2452:is the boundary of a disk containing
885:for the 3.14... constant in his 1736
877:, where it was denoted by the letter
506:
7486:
7224:
7181:
7116:
6816:
6671:
6435:Euler, Leonhard (1707–1783) (1922).
5488:
521:'full angle') for turns. Covered in
432:), equal to the ratio of a circle's
36:
7087:
6481:Segner, Johann Andreas von (1761).
5083:Newtonian Dynamics: An Introduction
4503:Physical quantity § Components
1094: turn would be represented as
904:Introductio in analysin infinitorum
894:Introductio in analysin infinitorum
881:. Euler would later use the letter
303:, one turn also corresponds to one
122:tr, pla, rev, cyc
24:
7265:"package math - pkg.odin-lang.org"
6859:"On Pi Day, is 'pi' under attack?"
6501:
6154:
5679:"Chapter 8: Keeping Track of Time"
4551:
4541:
4335:International System of Quantities
3189:
1891:-sphere volume recurrence relation
1068:to represent the circle constant:
719:Pi § Adoption of the symbol π
491:
394:
25:
7613:
7563:
7461:The International System of Units
7187:
6487:(in Latin). Renger. p. 374.
6344:The American Mathematical Monthly
6213:"William Jones: The First Use of
5489:Paul, Matthias R. (2016-01-12) .
5032:Original version, current version
3079:
3045:
1270:In 2012, the educational website
1064:proposed to use the Greek letter
53:Draft:Tau (mathematical constant)
7397:from the original on 2013-09-28.
6714:Proceedings of the 2014 IEEE GEM
6409:English translation by Ian Bruce
6405:rationem diametri ad peripheriam
6299:English translation by Ian Bruce
6223:. McGraw–Hill. pp. 346–347.
4624:rev, r, cyc, c
4411:where 𝜑 denotes the measure of
4271:
1352:. For a more complete list, see
1154:
1140:is the number of radians in one
906:, Euler instead used the letter
700:equal parts for other values of
408:proposed using the Greek letter
41:
7341:from the original on 2019-07-22
7327:Harremoës, Peter (2018-11-17).
7134:from the original on 2023-07-18
7105:from the original on 2019-07-22
7076:from the original on 2019-07-22
7047:from the original on 2019-07-22
7022:from the original on 2019-07-29
7012:"math — Mathematical functions"
6993:from the original on 2019-07-22
6963:from the original on 2023-03-26
6934:from the original on 2023-07-18
6905:from the original on 2019-06-18
6873:from the original on 2018-12-19
6799:from the original on 2019-07-18
6639:
6628:from the original on 2019-07-18
6550:
6474:
6449:from the original on 2017-10-16
6428:
6377:
6315:
6283:from the original on 2016-04-01
6250:
5855:from the original on 2019-06-30
5778:Volksbildungshaus Wiener Urania
5677:Klein, Herbert Arthur (2012) .
5634:(1962). Chandler, M. H. (ed.).
5605:from the original on 2023-07-18
5556:from the original on 2023-07-18
5501:from the original on 2019-08-05
5471:from the original on 2019-08-06
5441:from the original on 2017-08-10
5431:"RE: newRPL: Handling of units"
5411:from the original on 2019-05-10
5378:from the original on 2019-08-06
5353:from the original on 2019-06-22
5300:Kurzweil, Peter (2013-03-09) .
5221:McMillan, Robert (2020-03-13).
5166:from the original on 2019-06-28
5136:from the original on 2023-07-18
5053:
5044:
5035:
5026:
1237:, contains a natural factor of
1001:. Crease used the Greek letter
610:
607:) as mode and unit since 2019.
498:
7359:Abbott, Stephen (April 2012).
7124:"std::f64::consts::TAU - Rust"
6594:The Mathematical Intelligencer
5940:Synopsis Palmariorum Matheseos
5791:Hayes, Eugene Nelson (1975) .
5749:10.1080/01621459.1922.10502455
5158:Hartl, Michael (2019-03-14) .
5017:
2574:
2568:
2497:
2491:
2397:
2391:
2350:
2344:
2299:
2293:
2249:
2243:
2182:
2176:
2144:
2138:
2108:
2102:
2070:
2064:
2032:
2026:
1991:
1985:
1955:
1949:
1917:
1911:
549:
532:(October 2010), the so-called
278:at its center. It is equal to
13:
1:
6841:10.1016/S0262-4079(11)60036-5
6785:Hartl, Michael (2010-03-14).
6646:Crease, Robert (2008-02-01).
5884:Barnes & Noble Publishing
5762:Schiffner, Friedrich (1965).
5080:Fitzpatrick, Richard (2021).
5066:
4425:International System of Units
3766:
3760:
933:
351:), rotating objects, and the
7380:10.4169/mathhorizons.19.4.34
7251:.NET Reference Documentation
6981:Coghlan, Nick (2017-02-25).
6221:A Source Book in Mathematics
6211:Smith, David Eugene (1929).
6142:
6077:
6012:
5943:. London: J. Wale. pp.
5897:Schwartzman, Steven (1994).
5582:WP 43S Reference Manual
5196:. 2011-06-30. Archived from
3260:Conversion of common angles
2478:Standard normal distribution
820:(pi over rho) to denote the
393:radians, some have proposed
32:360 degrees (disambiguation)
7:
4930:
1355:List of formulae involving
1027:{\displaystyle \psi =2\pi }
554:The scientific calculators
546:in the EU and Switzerland.
489:
50:It has been suggested that
10:
7618:
7016:Python 3.7.0 documentation
5695:Simon & Schuster, Inc.
5646:/ Rathbone Books Limited.
5642:(1 ed.). London, UK:
5533:WP 43S Owner's Manual
5264:(in German) (1 ed.).
1524:Circumference of a circle
1334:-promoter Peter Harremoës.
1289:Desmos graphing calculator
774:The meaning of the symbol
716:
656:Binary fractions of a turn
614:
29:
7361:"My Conversion to Tauism"
6983:"PEP 628 -- Add math.tau"
5405:Schweizerischer Bundesrat
5374:(in German). 2009-03-11.
5349:(in German). 1980-02-15.
5316:10.1007/978-3-322-92920-4
4650:
4646:
4628:
4620:
4610:
4605:
4432:quantity of dimension one
4319:
4307:
4295:
4285:
4280:
3756:
3289:
3269:
2230:Cauchy's integral formula
586:in 2017. An angular mode
544:legal unit of measurement
538:('full angle') is not an
233:
217:
182:
148:
144:
126:
118:
108:
103:
85:
80:
67:Proposed since July 2024.
7306:10.14736/kyb-2016-6-0943
6513:Encyclopaedia Brittanica
6384:Euler, Leonhard (1736).
6257:Euler, Leonhard (1727).
6197:; and by means thereof,
5687:Dover Publications, Inc.
5403:(in Swiss High German).
5010:
4692:In programming languages
2638:Stirling's approximation
652:carry milliturn scales.
267:measurement that is the
7329:"Al-Kashi's constant τ"
6758:10.1145/3325424.3330210
6584:Palais, Robert (2001).
6386:"Ch. 3 Prop. 34 Cor. 1"
6340:English translation in
5579:Bonin, Walter (2019) .
5530:Bonin, Walter (2019) .
5407:. 1994-11-23. 941.202.
4676:dimensional homogeneity
4413:rotational displacement
3101:reduced Planck constant
2445:{\displaystyle \gamma }
1767:with unit circumradius
824:of a circle (i.e., the
6654:. Institute of Physics
6170:
4957:Revolutions per minute
4597:revolutions per minute
4565:
4487:
4417:
4402:
3218:
3176:
3142:
3086:
3052:
3006:
2902:
2769:
2703:
2625:
2551:
2472:in the complex plane.
2466:
2446:
2425:
2327:
2189:
2115:
2039:
1962:
1869:
1817:
1712:
1661:
1590:
1556:
1476:
1439:
1028:
984:
942:Peter Harremoës (2010)
788:
753:
745:
737:
590:was suggested for the
534:
517:
472:dimensionless quantity
457:
422:
387:
340:revolutions per minute
7592:Mathematical concepts
7212:Java 19 documentation
6953:"Supported Functions"
6236:"Pi through the ages"
6234:Veling, Anne (2001).
6217:for the Circle Ratio"
6171:
5794:Trackers of the Skies
5491:"RE: WP-32S in 2016?"
4899:std::f64::consts::TAU
4566:
4488:
4403:
4357:
4353:number of revolutions
3221:One turn is equal to
3197:
3177:
3143:
3087:
3053:
3007:
2903:
2770:
2704:
2626:
2552:
2467:
2447:
2426:
2328:
2190:
2116:
2040:
1963:
1870:
1818:
1713:
1662:
1591:
1557:
1477:
1440:
1115: rad instead of
1029:
985:
789:
751:
743:
726:
570:in 2016, and for the
458:
456:{\displaystyle 2\pi }
423:
421:{\displaystyle \tau }
388:
386:{\displaystyle 2\pi }
345:electromagnetic coils
7587:Units of plane angle
6928:blog.khanacademy.org
6601:(3). New York, USA:
6414:10 June 2016 at the
6304:10 June 2016 at the
5978:
4578:(s). Common related
4528:
4511:rotational frequency
4445:
4369:
3153:
3116:
3063:
3026:
2913:
2792:
2714:
2645:
2562:
2485:
2456:
2436:
2338:
2237:
2125:
2051:
1972:
1898:
1828:
1773:
1672:
1631:
1567:
1530:
1450:
1413:
1009:
957:
945:Michael Hartl (2010)
787:{\displaystyle \pi }
778:
666:, also known as the
511:The German standard
444:
412:
402:with a single letter
374:
370:Because one turn is
60:into this article. (
6898:Scientific American
6833:2011NewSc.209...23A
6787:"The Tau Manifesto"
5691:Courier Corporation
5401:Einheitenverordnung
5328:. 978-3-322-92921-1
5230:Wall Street Journal
5160:"The Tau Manifesto"
5005:Twist (mathematics)
4967:Spat (angular unit)
4641:... is equal to ...
3261:
1391:Angle subtended by
1365:
1348:is used instead of
1184:is used instead of
1170:visually resembles
1041:, Θ, to represent 2
932:Joseph Lindenburg (
542:. However, it is a
139:... is equal to ...
104:General information
7518:"ISO 80000-3:2006"
7269:Odin documentation
7175:Unreal Engine Docs
6648:"Constant failure"
6611:10.1007/bf03026846
6166:
6139:
6117:
6095:
6074:
6052:
6030:
6009:
5994:
5851:. blogs.msdn.com.
5465:newRPL User Manual
5145:(1+iii+32+1 pages)
4767:math_constants.Tau
4672:dimensionless unit
4660:
4652:
4580:units of frequency
4561:
4483:
4398:
3259:
3219:
3172:
3167:
3138:
3133:
3082:
3077:
3048:
3043:
3002:
2994:
2963:
2926:
2898:
2890:
2880:
2852:
2842:
2808:
2765:
2733:
2699:
2667:
2621:
2590:
2547:
2516:
2462:
2442:
2421:
2367:
2323:
2269:
2185:
2155:
2111:
2035:
2005:
1958:
1865:
1859:
1813:
1807:
1760:Area of a regular
1708:
1696:
1657:
1645:
1586:
1581:
1552:
1547:
1472:
1465:
1435:
1428:
1364:
1024:
999:John Horton Conway
980:
939:John Fisher (2004)
784:
754:
746:
738:
650:satellite watching
617:Angle § Units
507:EU and Switzerland
453:
418:
383:
329:units of frequency
327:). Common related
243:
235:
227:
219:
192:
184:
158:
150:
7571:The Tau Manifesto
7491:(2008 ed.).
7474:978-92-822-2272-0
7128:doc.rust-lang.org
6855:Landau, Elizabeth
6145:
6138:
6116:
6094:
6080:
6073:
6051:
6029:
6015:
6008:
5993:
5845:Hargreaves, Shawn
5776:. Wien, Austria:
5764:Wähnl, Maria Emma
5097:978-1-000-50953-3
4952:Angle of rotation
4928:
4927:
4774:Not yet released
4680:kinds of quantity
4668:
4667:
4629:Conversions
4591:cycles per second
4576:reciprocal second
4559:
4480:
4462:
4461:
4396:
4393:
4349:physical quantity
4331:
4330:
4266:
4265:
3187:
3186:
3109:Angular frequency
3000:
2969:
2939:
2896:
2858:
2821:
2785:th roots of unity
2753:
2738:
2687:
2672:
2617:
2592:
2591:
2543:
2518:
2517:
2465:{\displaystyle a}
2412:
2373:
2314:
2275:
2084:
1931:
1863:
1845:
1811:
1790:
1691:
1598:The length of an
1470:
1463:
1433:
1426:
494:for the formula.)
480:, defined as the
334:cycles per second
249:
248:
127:Conversions
93:Counterclockwise
74:
73:
69:
16:(Redirected from
7609:
7557:
7556:
7554:
7553:
7539:
7533:
7532:
7530:
7529:
7514:
7505:
7502:
7500:
7499:
7484:
7478:
7477:
7466:
7456:
7450:
7446:
7444:
7443:
7428:
7417:
7416:
7405:
7399:
7398:
7396:
7365:
7356:
7350:
7349:
7347:
7346:
7340:
7333:
7324:
7318:
7317:
7299:
7279:
7273:
7272:
7261:
7255:
7254:
7247:"Math.Tau Field"
7243:
7237:
7236:
7222:
7216:
7215:
7204:
7198:
7197:
7194:bugs.openjdk.org
7185:
7179:
7178:
7167:
7161:
7160:
7149:
7143:
7142:
7140:
7139:
7120:
7114:
7113:
7111:
7110:
7091:
7085:
7084:
7082:
7081:
7062:
7056:
7055:
7053:
7052:
7037:
7031:
7030:
7028:
7027:
7008:
7002:
7001:
6999:
6998:
6978:
6972:
6971:
6969:
6968:
6949:
6943:
6942:
6940:
6939:
6924:"Happy Tau Day!"
6920:
6914:
6913:
6911:
6910:
6888:
6882:
6881:
6879:
6878:
6851:
6845:
6844:
6814:
6808:
6807:
6805:
6804:
6798:
6791:
6782:
6776:
6775:
6773:
6772:
6752:(Keynote): 1–2.
6738:
6732:
6731:
6729:
6728:
6702:
6696:
6694:
6692:
6691:
6685:
6679:. Archived from
6678:
6669:
6663:
6662:
6660:
6659:
6643:
6637:
6636:
6634:
6633:
6627:
6590:
6581:
6572:
6571:
6569:
6568:
6554:
6548:
6547:
6530:
6524:
6523:
6521:
6520:
6505:
6499:
6498:
6496:
6492:
6478:
6472:
6471:
6465:
6457:
6455:
6454:
6432:
6426:
6424:
6407:
6404:
6381:
6375:
6374:
6371:
6339:
6337:
6319:
6313:
6311:
6297:
6295:
6289:
6288:
6282:
6263:
6254:
6248:
6247:
6242:. Archived from
6231:
6225:
6224:
6216:
6208:
6205:
6186:
6175:
6173:
6172:
6167:
6146:
6141:
6140:
6137:
6136:
6124:
6118:
6115:
6114:
6102:
6098:
6096:
6087:
6081:
6076:
6075:
6072:
6071:
6059:
6053:
6050:
6049:
6037:
6033:
6031:
6022:
6016:
6011:
6010:
6001:
5995:
5986:
5982:
5931:
5925:
5924:
5920:978-0-88385511-9
5904:
5894:
5888:
5887:
5870:
5864:
5863:
5861:
5860:
5841:
5835:
5834:
5832:
5831:
5809:
5803:
5802:
5788:
5782:
5781:
5759:
5753:
5752:
5743:(137): 108–109.
5730:
5724:
5722:
5720:
5719:
5704:978-0-48614497-9
5697:). p. 102.
5674:
5665:
5663:
5641:
5628:
5619:
5613:
5611:
5610:
5604:
5595:978-1-72950106-1
5587:
5576:
5570:
5564:
5562:
5561:
5555:
5546:978-1-72950098-9
5538:
5527:
5521:
5520:
5507:
5506:
5486:
5480:
5479:
5477:
5476:
5456:
5450:
5449:
5447:
5446:
5426:
5420:
5419:
5417:
5416:
5393:
5387:
5386:
5384:
5383:
5368:
5362:
5361:
5359:
5358:
5343:
5337:
5336:
5334:
5333:
5325:978-3-32292920-4
5297:
5291:
5290:
5288:
5287:
5279:978-3-32283606-9
5255:
5249:
5248:
5246:
5245:
5226:
5218:
5209:
5208:
5206:
5205:
5184:
5175:
5174:
5172:
5171:
5155:
5146:
5144:
5142:
5141:
5135:
5124:
5114:
5108:
5107:
5105:
5104:
5077:
5060:
5057:
5051:
5048:
5042:
5039:
5033:
5030:
5024:
5021:
5000:Modulo operation
4979:
4962:Repeating circle
4946:Cycle per second
4731:System.MathF.Tau
4700:
4699:
4697:the same value.
4661:
4653:
4603:
4602:
4570:
4568:
4567:
4562:
4560:
4558:
4554:
4548:
4544:
4538:
4520:
4492:
4490:
4489:
4484:
4482:
4481:
4478:
4463:
4459:
4455:
4407:
4405:
4404:
4399:
4397:
4395:
4394:
4391:
4379:
4278:
4277:
4255:
4234:
4232:
4231:
4228:
4225:
4224:
4213:
4211:
4210:
4207:
4204:
4195:
4193:
4192:
4189:
4186:
4169:
4163:
4161:
4160:
4157:
4154:
4145:
4143:
4142:
4139:
4136:
4119:
4117:
4116:
4113:
4110:
4109:
4098:
4096:
4095:
4092:
4089:
4080:
4078:
4077:
4074:
4071:
4061:
4059:
4058:
4055:
4052:
4048:
4037:
4035:
4034:
4031:
4028:
4027:
4016:
4014:
4013:
4010:
4007:
3998:
3996:
3995:
3992:
3989:
3972:
3970:
3969:
3966:
3963:
3962:
3952:
3950:
3949:
3946:
3943:
3934:
3932:
3931:
3928:
3925:
3908:
3906:
3905:
3902:
3899:
3898:
3887:
3885:
3884:
3881:
3878:
3869:
3867:
3866:
3863:
3860:
3850:
3848:
3847:
3844:
3841:
3837:
3826:
3824:
3823:
3820:
3817:
3816:
3806:
3804:
3803:
3800:
3797:
3788:
3786:
3785:
3782:
3779:
3768:
3762:
3753:
3751:
3750:
3749:
3744:
3741:
3724:
3722:
3721:
3718:
3715:
3714:
3704:
3702:
3701:
3698:
3695:
3686:
3684:
3683:
3680:
3677:
3660:
3658:
3657:
3654:
3651:
3650:
3640:
3638:
3637:
3634:
3631:
3622:
3620:
3619:
3616:
3613:
3603:
3601:
3600:
3597:
3594:
3590:
3579:
3577:
3576:
3573:
3570:
3569:
3559:
3557:
3556:
3553:
3550:
3541:
3539:
3538:
3535:
3532:
3515:
3513:
3512:
3509:
3506:
3505:
3495:
3493:
3492:
3489:
3486:
3477:
3475:
3474:
3471:
3468:
3458:
3456:
3455:
3452:
3449:
3445:
3434:
3432:
3431:
3428:
3425:
3424:
3414:
3412:
3411:
3408:
3405:
3396:
3394:
3393:
3390:
3387:
3377:
3375:
3374:
3371:
3368:
3364:
3353:
3351:
3350:
3347:
3344:
3343:
3333:
3331:
3330:
3327:
3324:
3315:
3313:
3312:
3309:
3306:
3262:
3258:
3243:
3242:
3239:
3236:
3233:
3227:
3216:
3181:
3179:
3178:
3173:
3168:
3147:
3145:
3144:
3139:
3134:
3098:
3091:
3089:
3088:
3083:
3078:
3057:
3055:
3054:
3049:
3044:
3011:
3009:
3008:
3003:
3001:
2996:
2995:
2984:
2970:
2965:
2964:
2953:
2942:
2941:
2940:
2932:
2927:
2907:
2905:
2904:
2899:
2897:
2892:
2891:
2881:
2873:
2859:
2854:
2853:
2843:
2835:
2824:
2823:
2822:
2814:
2809:
2784:
2774:
2772:
2771:
2766:
2764:
2763:
2758:
2754:
2746:
2739:
2734:
2727:
2708:
2706:
2705:
2700:
2698:
2697:
2692:
2688:
2680:
2673:
2668:
2658:
2630:
2628:
2627:
2622:
2620:
2619:
2618:
2613:
2612:
2603:
2593:
2585:
2581:
2556:
2554:
2553:
2548:
2546:
2545:
2544:
2539:
2538:
2529:
2519:
2508:
2504:
2471:
2469:
2468:
2463:
2451:
2449:
2448:
2443:
2430:
2428:
2427:
2422:
2413:
2411:
2400:
2386:
2384:
2383:
2374:
2372:
2368:
2357:
2332:
2330:
2329:
2324:
2315:
2313:
2302:
2288:
2286:
2285:
2276:
2274:
2270:
2256:
2224:
2210:
2194:
2192:
2191:
2186:
2175:
2174:
2156:
2137:
2136:
2120:
2118:
2117:
2112:
2101:
2100:
2085:
2077:
2063:
2062:
2044:
2042:
2041:
2036:
2025:
2024:
2006:
1984:
1983:
1967:
1965:
1964:
1959:
1948:
1947:
1932:
1924:
1910:
1909:
1890:
1884:
1874:
1872:
1871:
1866:
1864:
1854:
1846:
1838:
1822:
1820:
1819:
1814:
1812:
1799:
1791:
1783:
1764:
1754:
1750:
1748:
1747:
1744:
1741:
1729:
1717:
1715:
1714:
1709:
1707:
1706:
1697:
1692:
1684:
1666:
1664:
1663:
1658:
1656:
1655:
1646:
1624:Area of a circle
1617:
1607:
1595:
1593:
1592:
1587:
1582:
1561:
1559:
1558:
1553:
1548:
1519:
1517:
1515:
1514:
1511:
1508:
1501:
1499:
1498:
1495:
1492:
1481:
1479:
1478:
1473:
1471:
1468:
1466:
1464:
1456:
1444:
1442:
1441:
1436:
1434:
1431:
1429:
1427:
1419:
1406:
1404:
1403:
1400:
1397:
1383:
1375:
1366:
1363:
1358:
1351:
1347:
1333:
1286:
1279:
1265:
1252:
1250:
1249:
1246:
1243:
1236:
1231:
1229:
1228:
1225:
1222:
1210:
1206:
1199:
1192:Euler's identity
1189:
1183:
1173:
1169:
1165:
1164:
1161:
1160:
1147:
1139:
1135:
1134:
1132:
1131:
1128:
1125:
1114:
1113:
1111:
1110:
1107:
1104:
1093:
1091:
1090:
1087:
1084:
1077:
1056:
1052:
1044:
1033:
1031:
1030:
1025:
995:Robert P. Crease
989:
987:
986:
981:
952:
935:
927:
926:
917:
913:
909:
884:
880:
857:
853:
852:
850:
849:
844:
841:
830:William Oughtred
819:
818:
816:
815:
810:
807:
793:
791:
790:
785:
762:
761:
735:
703:
699:
691:
689:
688:
685:
682:
624:
604:
597:
537:
531:
520:
495:
462:
460:
459:
454:
427:
425:
424:
419:
401:
392:
390:
389:
384:
363:, respectively;
286:
244:
236:
228:
220:
213:
211:
207:
199:
193:
185:
178:
176:
173:
165:
159:
151:
90:
78:
77:
65:
45:
44:
37:
21:
7617:
7616:
7612:
7611:
7610:
7608:
7607:
7606:
7577:
7576:
7566:
7561:
7560:
7551:
7549:
7541:
7540:
7536:
7527:
7525:
7516:
7515:
7508:
7497:
7495:
7485:
7481:
7475:
7464:
7458:
7457:
7453:
7441:
7439:
7430:
7429:
7420:
7408:
7406:
7402:
7394:
7363:
7357:
7353:
7344:
7342:
7338:
7331:
7325:
7321:
7280:
7276:
7263:
7262:
7258:
7245:
7244:
7240:
7223:
7219:
7206:
7205:
7201:
7186:
7182:
7169:
7168:
7164:
7151:
7150:
7146:
7137:
7135:
7122:
7121:
7117:
7108:
7106:
7093:
7092:
7088:
7079:
7077:
7064:
7063:
7059:
7050:
7048:
7039:
7038:
7034:
7025:
7023:
7010:
7009:
7005:
6996:
6994:
6979:
6975:
6966:
6964:
6957:help.desmos.com
6951:
6950:
6946:
6937:
6935:
6922:
6921:
6917:
6908:
6906:
6889:
6885:
6876:
6874:
6852:
6848:
6815:
6811:
6802:
6800:
6796:
6789:
6783:
6779:
6770:
6768:
6739:
6735:
6726:
6724:
6703:
6699:
6689:
6687:
6683:
6676:
6670:
6666:
6657:
6655:
6644:
6640:
6631:
6629:
6625:
6603:Springer-Verlag
6588:
6582:
6575:
6566:
6564:
6556:
6555:
6551:
6534:Euler, Leonhard
6531:
6527:
6518:
6516:
6507:
6506:
6502:
6494:
6490:
6479:
6475:
6459:
6458:
6452:
6450:
6433:
6429:
6419:
6416:Wayback Machine
6399:
6382:
6378:
6369:
6356:10.2307/2973441
6335:
6320:
6316:
6309:
6306:Wayback Machine
6293:
6286:
6284:
6280:
6261:
6255:
6251:
6232:
6228:
6214:
6203:
6177:
6176:
6132:
6128:
6122:
6110:
6106:
6100:
6099:
6097:
6085:
6067:
6063:
6057:
6045:
6041:
6035:
6034:
6032:
6020:
5999:
5984:
5983:
5981:
5979:
5976:
5975:
5974:
5951:. p. 263:
5932:
5928:
5921:
5895:
5891:
5879:A History of Pi
5871:
5867:
5858:
5856:
5842:
5838:
5829:
5827:
5811:
5810:
5806:
5789:
5785:
5760:
5756:
5731:
5727:
5717:
5715:
5705:
5693:(originally by
5675:
5668:
5629:
5622:
5608:
5606:
5602:
5596:
5585:
5577:
5573:
5559:
5557:
5553:
5547:
5536:
5528:
5524:
5504:
5502:
5487:
5483:
5474:
5472:
5457:
5453:
5444:
5442:
5427:
5423:
5414:
5412:
5395:
5394:
5390:
5381:
5379:
5370:
5369:
5365:
5356:
5354:
5345:
5344:
5340:
5331:
5329:
5326:
5310:. p. 403.
5308:Springer-Verlag
5298:
5294:
5285:
5283:
5280:
5272:. p. 421.
5270:Springer-Verlag
5256:
5252:
5243:
5241:
5219:
5212:
5203:
5201:
5193:Telegraph India
5186:
5185:
5178:
5169:
5167:
5156:
5149:
5139:
5137:
5133:
5122:
5116:
5115:
5111:
5102:
5100:
5098:
5090:. p. 116.
5078:
5074:
5069:
5064:
5063:
5058:
5054:
5049:
5045:
5040:
5036:
5031:
5027:
5022:
5018:
5013:
4974:
4933:
4727:System.Math.Tau
4694:
4659:
4651:
4550:
4549:
4540:
4539:
4537:
4529:
4526:
4525:
4518:
4499:
4477:
4473:
4454:
4446:
4443:
4442:
4390:
4383:
4378:
4370:
4367:
4366:
4298:
4288:
4274:
4268:
4253:
4229:
4226:
4222:
4220:
4219:
4217:
4208:
4205:
4202:
4201:
4199:
4190:
4187:
4184:
4183:
4181:
4167:
4158:
4155:
4152:
4151:
4149:
4140:
4137:
4134:
4133:
4131:
4114:
4111:
4107:
4105:
4104:
4102:
4093:
4090:
4087:
4086:
4084:
4075:
4072:
4069:
4068:
4066:
4056:
4053:
4050:
4049:
4046:
4044:
4032:
4029:
4025:
4023:
4022:
4020:
4011:
4008:
4005:
4004:
4002:
3993:
3990:
3987:
3986:
3984:
3967:
3964:
3960:
3959:
3958:
3956:
3947:
3944:
3941:
3940:
3938:
3929:
3926:
3923:
3922:
3920:
3903:
3900:
3896:
3894:
3893:
3891:
3882:
3879:
3876:
3875:
3873:
3864:
3861:
3858:
3857:
3855:
3845:
3842:
3839:
3838:
3835:
3833:
3821:
3818:
3814:
3813:
3812:
3810:
3801:
3798:
3795:
3794:
3792:
3783:
3780:
3777:
3776:
3774:
3747:
3745:
3742:
3739:
3738:
3736:
3719:
3716:
3712:
3711:
3710:
3708:
3699:
3696:
3693:
3692:
3690:
3681:
3678:
3675:
3674:
3672:
3655:
3652:
3648:
3647:
3646:
3644:
3635:
3632:
3629:
3628:
3626:
3617:
3614:
3611:
3610:
3608:
3598:
3595:
3592:
3591:
3588:
3586:
3574:
3571:
3567:
3566:
3565:
3563:
3554:
3551:
3548:
3547:
3545:
3536:
3533:
3530:
3529:
3527:
3510:
3507:
3503:
3502:
3501:
3499:
3490:
3487:
3484:
3483:
3481:
3472:
3469:
3466:
3465:
3463:
3453:
3450:
3447:
3446:
3443:
3441:
3429:
3426:
3422:
3421:
3420:
3418:
3409:
3406:
3403:
3402:
3400:
3391:
3388:
3385:
3384:
3382:
3372:
3369:
3366:
3365:
3362:
3360:
3348:
3345:
3341:
3340:
3339:
3337:
3328:
3325:
3322:
3321:
3319:
3310:
3307:
3304:
3303:
3301:
3240:
3237:
3234:
3231:
3229:
3222:
3211:
3192:
3190:Unit conversion
3162:
3154:
3151:
3150:
3125:
3117:
3114:
3113:
3094:
3072:
3064:
3061:
3060:
3035:
3027:
3024:
3023:
3019:Planck constant
2989:
2985:
2983:
2958:
2954:
2952:
2931:
2921:
2920:
2916:
2914:
2911:
2910:
2885:
2875:
2874:
2872:
2847:
2837:
2836:
2834:
2813:
2800:
2799:
2795:
2793:
2790:
2789:
2782:
2759:
2745:
2741:
2740:
2728:
2726:
2715:
2712:
2711:
2693:
2679:
2675:
2674:
2659:
2657:
2646:
2643:
2642:
2608:
2604:
2602:
2598:
2594:
2580:
2563:
2560:
2559:
2534:
2530:
2528:
2524:
2520:
2503:
2486:
2483:
2482:
2457:
2454:
2453:
2437:
2434:
2433:
2401:
2387:
2385:
2379:
2375:
2362:
2361:
2356:
2339:
2336:
2335:
2303:
2289:
2287:
2281:
2277:
2261:
2260:
2255:
2238:
2235:
2234:
2218:
2212:
2211:
2204:
2198:
2164:
2160:
2150:
2132:
2128:
2126:
2123:
2122:
2090:
2086:
2076:
2058:
2054:
2052:
2049:
2048:
2014:
2010:
1997:
1979:
1975:
1973:
1970:
1969:
1937:
1933:
1923:
1905:
1901:
1899:
1896:
1895:
1886:
1882:
1853:
1837:
1829:
1826:
1825:
1798:
1782:
1774:
1771:
1770:
1762:
1745:
1742:
1739:
1738:
1736:
1731:
1725:
1702:
1698:
1683:
1681:
1673:
1670:
1669:
1651:
1647:
1640:
1632:
1629:
1628:
1609:
1603:
1576:
1568:
1565:
1564:
1539:
1531:
1528:
1527:
1512:
1509:
1506:
1505:
1503:
1496:
1493:
1488:
1487:
1485:
1484:
1467:
1455:
1453:
1451:
1448:
1447:
1430:
1418:
1416:
1414:
1411:
1410:
1401:
1398:
1395:
1394:
1392:
1379:
1373:
1356:
1349:
1339:
1331:
1284:
1275:
1261:
1247:
1244:
1241:
1240:
1238:
1226:
1223:
1220:
1219:
1217:
1212:
1208:
1201:
1194:
1185:
1179:
1171:
1167:
1166:sound. Second,
1157:
1153:
1145:
1137:
1129:
1126:
1120:
1119:
1117:
1116:
1108:
1105:
1099:
1098:
1096:
1095:
1088:
1085:
1082:
1081:
1079:
1069:
1054:
1050:
1042:
1010:
1007:
1006:
958:
955:
954:
950:
924:
922:
915:
911:
907:
882:
878:
855:
845:
842:
837:
836:
834:
833:
811:
808:
803:
802:
800:
799:
779:
776:
775:
759:
757:
733:
721:
713:
701:
697:
686:
683:
680:
679:
677:
622:
619:
613:
602:
595:
589:
552:
525:
509:
501:
445:
442:
441:
413:
410:
409:
396:
375:
372:
371:
365:metric prefixes
279:
269:angular measure
263:) is a unit of
242:
234:
226:
218:
209:
205:
203:
201:
194:
191:
183:
174:
171:
169:
167:
160:
157:
149:
99:
98:
70:
46:
42:
35:
28:
23:
22:
18:Number of turns
15:
12:
11:
5:
7615:
7605:
7604:
7599:
7594:
7589:
7575:
7574:
7565:
7564:External links
7562:
7559:
7558:
7534:
7506:
7479:
7473:
7451:
7434:(2 ed.).
7418:
7400:
7351:
7319:
7290:(6): 943–966.
7274:
7256:
7238:
7217:
7199:
7180:
7162:
7144:
7115:
7086:
7057:
7041:"Perl 6 terms"
7032:
7003:
6973:
6944:
6930:. 2012-06-28.
6915:
6883:
6857:(2011-03-14).
6846:
6809:
6777:
6733:
6697:
6664:
6638:
6573:
6549:
6525:
6500:
6473:
6427:
6376:
6314:
6249:
6246:on 2009-07-02.
6226:
6178:3.14159, &
6165:
6162:
6159:
6156:
6152:
6149:
6144:
6135:
6131:
6127:
6121:
6113:
6109:
6105:
6093:
6090:
6084:
6079:
6070:
6066:
6062:
6056:
6048:
6044:
6040:
6028:
6025:
6019:
6014:
6007:
6004:
5998:
5992:
5989:
5961:of particular
5935:Jones, William
5926:
5919:
5889:
5874:Beckmann, Petr
5865:
5836:
5804:
5799:Academic Press
5783:
5754:
5739:. Short Note.
5725:
5703:
5666:
5620:
5594:
5571:
5545:
5522:
5481:
5451:
5421:
5388:
5363:
5338:
5324:
5292:
5278:
5250:
5210:
5176:
5147:
5125:. London, UK:
5109:
5096:
5071:
5070:
5068:
5065:
5062:
5061:
5052:
5043:
5034:
5025:
5015:
5014:
5012:
5009:
5008:
5007:
5002:
4997:
4990:
4985:
4964:
4959:
4954:
4949:
4939:
4932:
4929:
4926:
4925:
4922:
4919:
4914:
4908:
4907:
4904:
4901:
4896:
4890:
4889:
4887:
4885:
4876:
4870:
4869:
4866:
4863:
4858:
4852:
4851:
4848:
4845:
4836:
4830:
4829:
4826:
4823:
4818:
4812:
4811:
4808:
4805:
4800:
4794:
4793:
4790:
4787:
4782:
4776:
4775:
4772:
4769:
4764:
4758:
4757:
4754:
4751:
4746:
4740:
4739:
4736:
4733:
4724:
4714:
4713:
4712:Year Released
4710:
4707:
4704:
4693:
4690:
4666:
4665:
4657:
4648:
4647:
4644:
4643:
4638:
4631:
4630:
4626:
4625:
4622:
4618:
4617:
4612:
4608:
4607:
4572:
4571:
4557:
4553:
4547:
4543:
4536:
4533:
4515:rate of change
4497:
4494:
4493:
4476:
4472:
4469:
4466:
4458:
4453:
4450:
4409:
4408:
4389:
4386:
4382:
4377:
4374:
4329:
4328:
4323:
4317:
4316:
4311:
4305:
4304:
4299:
4297:Common symbols
4296:
4293:
4292:
4289:
4286:
4283:
4282:
4273:
4270:
4264:
4263:
4260:
4257:
4250:
4247:
4243:
4242:
4239:
4236:
4215:
4197:
4178:
4177:
4174:
4171:
4165:
4147:
4128:
4127:
4124:
4121:
4100:
4082:
4063:
4062:
4042:
4039:
4018:
4000:
3981:
3980:
3977:
3974:
3954:
3936:
3917:
3916:
3913:
3910:
3889:
3871:
3852:
3851:
3831:
3828:
3808:
3790:
3771:
3770:
3764:
3758:
3755:
3733:
3732:
3729:
3726:
3706:
3688:
3669:
3668:
3665:
3662:
3642:
3624:
3605:
3604:
3584:
3581:
3561:
3543:
3524:
3523:
3520:
3517:
3497:
3479:
3460:
3459:
3439:
3436:
3416:
3398:
3379:
3378:
3358:
3355:
3335:
3317:
3298:
3297:
3294:
3291:
3288:
3284:
3283:
3278:
3273:
3268:
3191:
3188:
3185:
3184:
3182:
3171:
3166:
3161:
3158:
3148:
3137:
3132:
3129:
3124:
3121:
3111:
3105:
3104:
3092:
3081:
3076:
3071:
3068:
3058:
3047:
3042:
3039:
3034:
3031:
3021:
3015:
3014:
3012:
2999:
2993:
2988:
2982:
2979:
2976:
2973:
2968:
2962:
2957:
2951:
2948:
2945:
2938:
2935:
2930:
2925:
2919:
2908:
2895:
2889:
2884:
2879:
2871:
2868:
2865:
2862:
2857:
2851:
2846:
2841:
2833:
2830:
2827:
2820:
2817:
2812:
2807:
2804:
2798:
2787:
2778:
2777:
2775:
2762:
2757:
2752:
2749:
2744:
2737:
2732:
2725:
2722:
2719:
2709:
2696:
2691:
2686:
2683:
2678:
2671:
2666:
2663:
2656:
2653:
2650:
2640:
2634:
2633:
2631:
2616:
2611:
2607:
2601:
2597:
2589:
2584:
2579:
2576:
2573:
2570:
2567:
2557:
2542:
2537:
2533:
2527:
2523:
2515:
2512:
2507:
2502:
2499:
2496:
2493:
2490:
2480:
2474:
2473:
2461:
2441:
2431:
2420:
2417:
2410:
2407:
2404:
2399:
2396:
2393:
2390:
2382:
2378:
2371:
2366:
2360:
2355:
2352:
2349:
2346:
2343:
2333:
2322:
2319:
2312:
2309:
2306:
2301:
2298:
2295:
2292:
2284:
2280:
2273:
2268:
2265:
2259:
2254:
2251:
2248:
2245:
2242:
2232:
2226:
2225:
2216:
2202:
2196:
2184:
2181:
2178:
2173:
2170:
2167:
2163:
2159:
2154:
2149:
2146:
2143:
2140:
2135:
2131:
2110:
2107:
2104:
2099:
2096:
2093:
2089:
2083:
2080:
2075:
2072:
2069:
2066:
2061:
2057:
2046:
2034:
2031:
2028:
2023:
2020:
2017:
2013:
2009:
2004:
2001:
1996:
1993:
1990:
1987:
1982:
1978:
1957:
1954:
1951:
1946:
1943:
1940:
1936:
1930:
1927:
1922:
1919:
1916:
1913:
1908:
1904:
1893:
1878:
1877:
1875:
1862:
1858:
1852:
1849:
1844:
1841:
1836:
1833:
1823:
1810:
1806:
1803:
1797:
1794:
1789:
1786:
1781:
1778:
1768:
1757:
1756:
1720:The area of a
1718:
1705:
1701:
1695:
1690:
1687:
1680:
1677:
1667:
1654:
1650:
1644:
1639:
1636:
1626:
1620:
1619:
1596:
1585:
1580:
1575:
1572:
1562:
1551:
1546:
1543:
1538:
1535:
1525:
1521:
1520:
1482:
1462:
1459:
1445:
1425:
1422:
1408:
1388:
1387:
1384:
1376:
1370:
1336:
1335:
1328:
1281:
1023:
1020:
1017:
1014:
979:
976:
973:
970:
962:
947:
946:
943:
940:
937:
871:Leonhard Euler
862:mathematician
783:
712:
706:
660:compass points
641:protractor".
612:
609:
587:
551:
548:
518:plenus angulus
508:
505:
500:
497:
452:
449:
417:
382:
379:
357:straight angle
353:winding number
274:by a complete
247:
246:
240:
231:
230:
224:
215:
214:
189:
180:
179:
155:
146:
145:
142:
141:
136:
129:
128:
124:
123:
120:
116:
115:
110:
106:
105:
101:
100:
92:
91:
83:
82:
72:
71:
49:
47:
40:
26:
9:
6:
4:
3:
2:
7614:
7603:
7600:
7598:
7595:
7593:
7590:
7588:
7585:
7584:
7582:
7573:
7572:
7568:
7567:
7548:
7544:
7538:
7523:
7519:
7513:
7511:
7504:
7494:
7490:
7483:
7476:
7470:
7463:
7462:
7455:
7448:
7437:
7433:
7427:
7425:
7423:
7415:
7411:
7404:
7393:
7389:
7385:
7381:
7377:
7373:
7369:
7368:Math Horizons
7362:
7355:
7337:
7330:
7323:
7315:
7311:
7307:
7303:
7298:
7293:
7289:
7285:
7278:
7270:
7266:
7260:
7252:
7248:
7242:
7234:
7233:
7228:
7221:
7213:
7209:
7203:
7195:
7191:
7184:
7176:
7172:
7166:
7158:
7154:
7148:
7133:
7129:
7125:
7119:
7104:
7100:
7096:
7090:
7075:
7071:
7067:
7061:
7046:
7042:
7036:
7021:
7017:
7013:
7007:
6992:
6988:
6984:
6977:
6962:
6958:
6954:
6948:
6933:
6929:
6925:
6919:
6904:
6900:
6899:
6894:
6887:
6872:
6868:
6864:
6860:
6856:
6850:
6842:
6838:
6834:
6830:
6826:
6823:. Interview.
6822:
6821:
6820:New Scientist
6813:
6795:
6788:
6781:
6767:
6763:
6759:
6755:
6751:
6747:
6743:
6737:
6723:
6719:
6715:
6711:
6707:
6701:
6686:on 2023-07-18
6682:
6675:
6668:
6653:
6652:Physics World
6649:
6642:
6624:
6620:
6616:
6612:
6608:
6604:
6600:
6596:
6595:
6587:
6586:"Pi is Wrong"
6580:
6578:
6562:
6561:
6553:
6545:
6541:
6540:
6535:
6529:
6514:
6510:
6504:
6497:
6486:
6485:
6477:
6469:
6463:
6448:
6444:
6440:
6439:
6431:
6423:
6418: : "Let
6417:
6413:
6410:
6406:
6403:
6395:
6391:
6387:
6380:
6373:
6365:
6361:
6357:
6353:
6349:
6345:
6338:
6331:
6327:
6326:
6318:
6307:
6303:
6300:
6296:
6279:
6275:
6271:
6267:
6260:
6253:
6245:
6241:
6237:
6230:
6222:
6218:
6209:Reprinted in
6207:
6202:
6201:
6196:
6195:
6190:
6185:
6181:
6163:
6160:
6157:
6150:
6147:
6133:
6129:
6125:
6119:
6111:
6107:
6103:
6091:
6088:
6082:
6068:
6064:
6060:
6054:
6046:
6042:
6038:
6026:
6023:
6017:
6005:
6002:
5996:
5990:
5987:
5972:
5968:
5964:
5960:
5956:
5950:
5946:
5942:
5941:
5936:
5930:
5922:
5916:
5912:
5908:
5903:
5902:
5893:
5885:
5881:
5880:
5875:
5869:
5854:
5850:
5846:
5840:
5826:on 2008-06-28
5825:
5821:
5819:
5814:
5808:
5800:
5796:
5795:
5787:
5779:
5775:
5772:(in German).
5771:
5770:
5765:
5758:
5750:
5746:
5742:
5738:
5737:
5729:
5714:
5710:
5706:
5700:
5696:
5692:
5688:
5684:
5680:
5673:
5671:
5661:
5657:
5653:
5649:
5645:
5640:
5639:
5633:
5627:
5625:
5617:
5615:
5601:
5597:
5591:
5584:
5583:
5575:
5568:
5566:
5552:
5548:
5542:
5535:
5534:
5526:
5519:
5517:
5513:
5500:
5496:
5492:
5485:
5470:
5466:
5462:
5455:
5440:
5436:
5432:
5425:
5410:
5406:
5402:
5398:
5392:
5377:
5373:
5367:
5352:
5348:
5342:
5327:
5321:
5317:
5313:
5309:
5305:
5304:
5296:
5281:
5275:
5271:
5267:
5263:
5262:
5254:
5240:
5236:
5232:
5231:
5225:
5217:
5215:
5200:on 2013-07-13
5199:
5195:
5194:
5189:
5183:
5181:
5165:
5161:
5154:
5152:
5132:
5128:
5121:
5120:
5113:
5099:
5093:
5089:
5085:
5084:
5076:
5072:
5056:
5047:
5038:
5029:
5020:
5016:
5006:
5003:
5001:
4998:
4996:
4995:
4991:
4989:
4988:Unit interval
4986:
4983:
4978:
4972:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4947:
4943:
4940:
4938:
4935:
4934:
4923:
4920:
4918:
4915:
4913:
4910:
4909:
4905:
4902:
4900:
4897:
4895:
4892:
4891:
4888:
4886:
4884:
4880:
4877:
4875:
4872:
4871:
4867:
4864:
4862:
4859:
4857:
4854:
4853:
4849:
4846:
4844:
4840:
4837:
4835:
4832:
4831:
4827:
4824:
4822:
4819:
4817:
4814:
4813:
4809:
4806:
4804:
4801:
4799:
4796:
4795:
4791:
4788:
4786:
4783:
4781:
4778:
4777:
4773:
4770:
4768:
4765:
4763:
4760:
4759:
4755:
4752:
4750:
4747:
4745:
4742:
4741:
4737:
4734:
4732:
4728:
4725:
4723:
4719:
4716:
4715:
4711:
4709:First Version
4708:
4705:
4702:
4701:
4698:
4689:
4687:
4686:
4681:
4677:
4673:
4664:
4658:
4656:
4649:
4645:
4642:
4639:
4637:
4633:
4632:
4627:
4623:
4619:
4616:
4613:
4609:
4604:
4601:
4599:
4598:
4593:
4592:
4587:
4586:
4581:
4577:
4555:
4545:
4534:
4531:
4524:
4523:
4522:
4516:
4512:
4507:
4505:
4504:
4470:
4464:
4456:
4451:
4448:
4441:
4440:
4439:
4437:
4433:
4428:
4426:
4422:
4416:
4414:
4387:
4384:
4380:
4375:
4372:
4365:
4364:
4363:
4361:
4356:
4354:
4350:
4346:
4345:
4340:
4336:
4327:
4324:
4322:
4318:
4315:
4312:
4310:
4306:
4303:
4300:
4294:
4290:
4284:
4279:
4276:
4272:In the ISQ/SI
4269:
4261:
4258:
4251:
4248:
4245:
4244:
4240:
4237:
4216:
4198:
4180:
4179:
4175:
4172:
4166:
4148:
4130:
4129:
4125:
4122:
4101:
4083:
4065:
4064:
4043:
4040:
4019:
4001:
3983:
3982:
3978:
3975:
3955:
3937:
3919:
3918:
3914:
3911:
3890:
3872:
3854:
3853:
3832:
3829:
3809:
3791:
3773:
3772:
3765:
3759:
3735:
3734:
3730:
3727:
3707:
3689:
3671:
3670:
3666:
3663:
3643:
3625:
3607:
3606:
3585:
3582:
3562:
3544:
3526:
3525:
3521:
3518:
3498:
3480:
3462:
3461:
3440:
3437:
3417:
3399:
3381:
3380:
3359:
3356:
3336:
3318:
3300:
3299:
3295:
3292:
3286:
3285:
3282:
3279:
3277:
3274:
3272:
3267:
3264:
3263:
3257:
3255:
3251:
3247:
3226:
3215:
3209:
3205:
3201:
3200:circumference
3196:
3183:
3169:
3164:
3159:
3156:
3149:
3135:
3130:
3127:
3122:
3119:
3112:
3110:
3107:
3106:
3102:
3097:
3093:
3074:
3069:
3066:
3059:
3040:
3037:
3032:
3029:
3022:
3020:
3017:
3016:
3013:
2997:
2991:
2986:
2980:
2977:
2974:
2971:
2966:
2960:
2955:
2949:
2946:
2943:
2936:
2933:
2928:
2923:
2917:
2909:
2893:
2887:
2882:
2877:
2869:
2866:
2863:
2860:
2855:
2849:
2844:
2839:
2831:
2828:
2825:
2818:
2815:
2810:
2805:
2802:
2796:
2788:
2786:
2780:
2779:
2776:
2760:
2755:
2750:
2747:
2742:
2735:
2730:
2723:
2720:
2717:
2710:
2694:
2689:
2684:
2681:
2676:
2669:
2664:
2661:
2654:
2651:
2648:
2641:
2639:
2636:
2635:
2632:
2614:
2609:
2605:
2599:
2595:
2587:
2582:
2577:
2571:
2565:
2558:
2540:
2535:
2531:
2525:
2521:
2513:
2510:
2505:
2500:
2494:
2488:
2481:
2479:
2476:
2475:
2459:
2439:
2432:
2418:
2415:
2408:
2405:
2402:
2394:
2388:
2380:
2376:
2369:
2364:
2358:
2353:
2347:
2341:
2334:
2320:
2317:
2310:
2307:
2304:
2296:
2290:
2282:
2278:
2271:
2266:
2263:
2257:
2252:
2246:
2240:
2233:
2231:
2228:
2227:
2222:
2215:
2208:
2201:
2197:
2195:
2179:
2171:
2168:
2165:
2161:
2157:
2152:
2147:
2141:
2133:
2129:
2105:
2097:
2094:
2091:
2087:
2081:
2078:
2073:
2067:
2059:
2055:
2047:
2045:
2029:
2021:
2018:
2015:
2011:
2007:
2002:
1999:
1994:
1988:
1980:
1976:
1952:
1944:
1941:
1938:
1934:
1928:
1925:
1920:
1914:
1906:
1902:
1894:
1892:
1889:
1880:
1879:
1876:
1860:
1856:
1850:
1847:
1842:
1839:
1834:
1831:
1824:
1808:
1804:
1801:
1795:
1792:
1787:
1784:
1779:
1776:
1769:
1766:
1759:
1758:
1753:
1734:
1728:
1723:
1719:
1703:
1699:
1693:
1688:
1685:
1678:
1675:
1668:
1652:
1648:
1642:
1637:
1634:
1627:
1625:
1622:
1621:
1616:
1612:
1606:
1601:
1597:
1583:
1578:
1573:
1570:
1563:
1549:
1544:
1541:
1536:
1533:
1526:
1523:
1522:
1491:
1483:
1460:
1457:
1446:
1423:
1420:
1409:
1390:
1389:
1385:
1382:
1377:
1371:
1368:
1367:
1362:
1360:
1359:
1346:
1342:
1329:
1326:
1322:
1318:
1317:UE Blueprints
1314:
1310:
1306:
1302:
1298:
1294:
1290:
1283:The constant
1282:
1278:
1273:
1269:
1268:
1267:
1264:
1258:
1256:
1253:arising from
1235:
1215:
1204:
1197:
1193:
1188:
1182:
1177:
1176:Tau Manifesto
1163:
1152:begin with a
1151:
1143:
1124:
1103:
1076:
1072:
1067:
1063:
1062:Michael Hartl
1058:
1048:
1040:
1035:
1021:
1018:
1015:
1012:
1004:
1000:
996:
991:
977:
974:
971:
968:
960:
944:
941:
938:
931:
930:
929:
928:, including:
919:
905:
901:
897:
895:
890:
889:
876:
872:
867:
865:
864:William Jones
861:
848:
840:
831:
827:
826:circumference
823:
814:
806:
797:
796:David Gregory
781:
772:
770:
766:
765:circumference
750:
742:
731:
725:
720:
715:
711:
705:
695:
675:
671:
670:
669:binary radian
665:
664:binary degree
661:
657:
653:
651:
647:
642:
640:
636:
632:
628:
618:
608:
606:
605:
601:multiples of
593:
585:
581:
577:
573:
569:
565:
561:
560:HP Prime
557:
556:HP 39gII
547:
545:
541:
536:
529:
524:
519:
514:
504:
496:
493:
487:
483:
479:
478:
473:
469:
464:
450:
447:
439:
435:
434:circumference
431:
415:
407:
406:Michael Hartl
403:
400:
395:representing
380:
377:
368:
366:
362:
358:
354:
350:
346:
342:
341:
336:
335:
330:
326:
322:
318:
314:
310:
306:
302:
298:
294:
290:
285:
284:
277:
273:
270:
266:
262:
258:
254:
241:
239:
232:
225:
223:
216:
212:... mrad
198:
190:
188:
181:
164:
156:
154:
147:
143:
140:
137:
135:
131:
130:
125:
121:
117:
114:
111:
107:
102:
96:
89:
84:
79:
76:
68:
63:
59:
55:
54:
48:
39:
38:
33:
19:
7570:
7550:. Retrieved
7546:
7537:
7526:. Retrieved
7524:. 2001-08-31
7521:
7496:. Retrieved
7482:
7460:
7454:
7440:. Retrieved
7403:
7371:
7367:
7354:
7343:. Retrieved
7322:
7287:
7283:
7277:
7268:
7259:
7250:
7241:
7230:
7220:
7211:
7208:"Math class"
7202:
7193:
7188:Darcy, Joe.
7183:
7174:
7165:
7156:
7147:
7136:. Retrieved
7127:
7118:
7107:. Retrieved
7098:
7089:
7078:. Retrieved
7069:
7060:
7049:. Retrieved
7035:
7024:. Retrieved
7015:
7006:
6995:. Retrieved
6986:
6976:
6965:. Retrieved
6956:
6947:
6936:. Retrieved
6927:
6918:
6907:. Retrieved
6896:
6886:
6875:. Retrieved
6862:
6849:
6827:(2794): 23.
6824:
6818:
6812:
6801:. Retrieved
6780:
6769:. Retrieved
6749:
6736:
6725:. Retrieved
6713:
6700:
6688:. Retrieved
6681:the original
6667:
6656:. Retrieved
6651:
6641:
6630:. Retrieved
6598:
6592:
6565:. Retrieved
6559:
6552:
6543:
6538:
6528:
6517:. Retrieved
6515:. 2024-03-14
6512:
6503:
6488:
6483:
6476:
6451:. Retrieved
6437:
6430:
6421:
6401:
6397:
6389:
6379:
6367:
6350:(3): 75–84.
6347:
6343:
6333:
6324:
6317:
6291:
6285:. Retrieved
6269:
6268:(in Latin).
6265:
6252:
6244:the original
6239:
6229:
6220:
6198:
6192:
6188:
6183:
6179:
5970:
5966:
5962:
5958:
5954:
5952:
5939:
5929:
5900:
5892:
5878:
5868:
5857:. Retrieved
5839:
5828:. Retrieved
5824:the original
5816:
5807:
5793:
5786:
5773:
5767:
5757:
5740:
5734:
5728:
5716:. Retrieved
5682:
5637:
5607:. Retrieved
5581:
5574:
5558:. Retrieved
5532:
5525:
5509:
5503:. Retrieved
5494:
5484:
5473:. Retrieved
5464:
5454:
5443:. Retrieved
5434:
5424:
5413:. Retrieved
5400:
5391:
5380:. Retrieved
5366:
5355:. Retrieved
5341:
5330:. Retrieved
5302:
5295:
5284:. Retrieved
5260:
5253:
5242:. Retrieved
5228:
5202:. Retrieved
5198:the original
5191:
5168:. Retrieved
5138:. Retrieved
5118:
5112:
5101:. Retrieved
5082:
5075:
5055:
5046:
5037:
5028:
5019:
4992:
4976:
4944:(modern) or
4917:std.math.tau
4695:
4683:
4669:
4640:
4635:
4611:Unit of
4595:
4589:
4583:
4573:
4508:
4501:
4495:
4435:
4429:
4418:
4410:
4359:
4358:
4352:
4343:
4342:
4338:
4332:
4309:SI unit
4301:
4275:
4267:
3265:
3224:
3220:
3213:
3095:
2220:
2213:
2206:
2199:
2121:
1968:
1887:
1751:
1732:
1726:
1614:
1610:
1604:
1489:
1407:of a circle
1380:
1353:
1344:
1340:
1337:
1276:
1272:Khan Academy
1262:
1259:
1233:
1213:
1202:
1195:
1186:
1180:
1175:
1149:
1141:
1122:
1101:
1074:
1070:
1059:
1036:
992:
948:
920:
903:
892:
886:
874:
868:
846:
838:
812:
804:
773:
755:
714:
709:
673:
667:
663:
654:
643:
631:21′ 36″
620:
611:Subdivisions
599:
584:HP 40gs
580:HP 39gs
576:HP 49g+
572:hp 39g+
553:
510:
502:
499:Unit symbols
485:
476:
475:
465:
398:
369:
349:transformers
338:
332:
324:
320:
316:
315:) or to one
312:
308:
304:
301:angular unit
295:or 400
282:
260:
256:
252:
250:
196:
187:milliradians
177:... rad
162:
138:
133:
109:Unit of
75:
66:
51:
7284:Kybernetika
6742:Mann, Steve
6706:Mann, Steve
6194:John Machin
5963:Curve Lines
5723:(736 pages)
5664:(320 pages)
5632:Hoyle, Fred
5618:(271 pages)
5569:(314 pages)
5516:conversions
5268:, reprint:
4971:solid angle
4937:Ampere-turn
4706:Identifiers
4634:1 rev
4594:(cps), and
4421:ISO 80000-3
4351:defined as
4287:Other names
3210:is one) is
3204:unit circle
1327:, and Odin.
1255:integration
1144:, and both
900:unit circle
756:The number
592:WP 43S
568:HP 50g
550:Calculators
526: [
404:. In 2010,
361:right angle
291:, 360
265:plane angle
113:Plane angle
7602:1 (number)
7581:Categories
7552:2023-05-12
7528:2023-04-25
7498:2023-07-17
7449:(11 pages)
7442:2019-10-23
7345:2018-09-20
7297:1601.05179
7225:John-H-K.
7157:Godot Docs
7138:2020-10-09
7109:2019-08-05
7080:2019-08-05
7070:Processing
7051:2019-08-05
7026:2019-08-05
6997:2019-08-05
6987:Python.org
6967:2023-03-21
6938:2020-12-19
6909:2015-03-20
6877:2019-08-05
6803:2019-08-05
6771:2023-07-18
6727:2023-07-18
6695:(18 pages)
6690:2023-07-18
6658:2024-08-03
6632:2019-08-05
6567:2024-07-24
6519:2024-03-26
6453:2017-10-15
6294:I : π
6287:2017-10-15
6200:Van Ceulen
5909:. p.
5859:2019-08-05
5830:2019-08-05
5718:2019-08-06
5609:2019-08-05
5560:2019-08-05
5505:2019-08-05
5475:2019-08-07
5445:2019-08-05
5415:2013-01-01
5382:2019-08-06
5357:2019-08-06
5332:2015-08-14
5286:2015-08-14
5244:2020-05-21
5204:2019-08-05
5170:2013-09-14
5140:2023-07-18
5103:2023-04-25
5067:References
4982:steradians
4834:Processing
4655:Base units
4606:Revolution
4496:where {𝜑}
4045:133
1885:-ball and
1301:Processing
717:See also:
646:Fred Hoyle
639:percentage
635:protractor
615:See also:
535:Vollwinkel
523:DIN 1301-1
337:(cps) and
317:revolution
200: mrad
132:1 tr
7407:Sequence
7388:126179022
7374:(4): 34.
7314:119126029
6766:189926593
6619:120965049
6489:Si autem
6462:cite book
6420:1 :
6400:1 :
6240:veling.nl
6155:&
6148:−
6143:¯
6120:−
6078:¯
6055:−
6018:−
6013:¯
5997:−
5876:(1989) .
5638:Astronomy
5495:HP Museum
5435:HP Museum
5239:0099-9660
5088:CRC Press
4789:Godot 3.0
4471:φ
4457:φ
4392: rad
4388:π
4381:φ
4321:Dimension
3834:66
3587:33
3442:16
3252:, or 400
3165:τ
3157:ω
3131:π
3120:ω
3080:ℏ
3075:τ
3046:ℏ
3041:π
2992:τ
2981:
2961:τ
2950:
2924:τ
2888:π
2870:
2850:π
2832:
2806:π
2731:τ
2724:∼
2665:π
2655:∼
2600:−
2588:τ
2566:φ
2526:−
2514:π
2489:φ
2440:γ
2406:−
2381:γ
2377:∮
2365:τ
2308:−
2283:γ
2279:∮
2267:π
2169:−
2153:τ
2095:−
2019:−
2003:π
1942:−
1857:τ
1851:
1805:π
1796:
1724:of angle
1694:τ
1643:π
1602:of angle
1579:τ
1545:π
1469: rad
1458:τ
1432: rad
1421:π
1060:In 2010,
1022:π
1013:ψ
993:In 2008,
978:π
969:π
961:π
891:and 1748
888:Mechanica
832:had used
822:perimeter
782:π
451:π
416:τ
381:π
272:subtended
166: rad
95:rotations
7392:Archived
7336:Archived
7132:Archived
7103:Archived
7074:Archived
7045:Archived
7020:Archived
6991:Archived
6961:Archived
6932:Archived
6903:Archived
6871:Archived
6794:Archived
6623:Archived
6536:(1746).
6447:Archived
6412:Archived
6398:Denotet
6368:Letting
6302:Archived
6278:Archived
5937:(1706).
5853:Archived
5713:88-25858
5652:62065943
5600:Archived
5551:Archived
5499:Archived
5469:Archived
5439:Archived
5409:Archived
5376:Archived
5351:Archived
5164:Archived
5131:Archived
5129:. 2016.
4931:See also
4861:math.tau
4803:Math.TAU
4780:GDScript
4703:Language
4615:Rotation
4341:(symbol
4339:rotation
4314:Unitless
4281:Rotation
3361:5
3281:Gradians
3254:gradians
3228:(≈
1313:GDScript
873:'s 1727
566:for the
513:DIN 1315
477:rotation
319:(symbol
307:(symbol
299:. As an
297:gradians
255:(symbol
238:gradians
7547:iso.org
7414:A019692
7412::
6863:cnn.com
6829:Bibcode
6722:6462220
6605:: 7–8.
6364:2973441
6272:: 351.
6187:. This
5955:Lengths
5660:7419446
4948:(older)
4771:Curtiss
4744:Crystal
4600:(rpm).
4427:(SI).
4347:) is a
4337:(ISQ),
4333:In the
4249:𝜏 rad
4246:1 turn
4233:
4218:
4212:
4200:
4194:
4182:
4162:
4150:
4144:
4132:
4118:
4103:
4097:
4085:
4079:
4067:
4060:
4036:
4021:
4015:
4003:
3997:
3985:
3971:
3957:
3951:
3939:
3933:
3921:
3907:
3892:
3886:
3874:
3868:
3856:
3849:
3825:
3811:
3805:
3793:
3787:
3775:
3752:
3737:
3723:
3709:
3703:
3691:
3685:
3673:
3659:
3645:
3639:
3627:
3621:
3609:
3602:
3578:
3564:
3558:
3546:
3540:
3528:
3514:
3500:
3494:
3482:
3476:
3464:
3457:
3433:
3419:
3413:
3401:
3395:
3383:
3376:
3352:
3338:
3332:
3320:
3314:
3302:
3287:0 turn
3276:Degrees
3271:Radians
3250:degrees
3246:radians
3206:(whose
3202:of the
3099:is the
1749:
1737:
1516:
1504:
1500:
1486:
1405:
1393:
1369:Formula
1251:
1239:
1230:
1218:
1133:
1118:
1112:
1097:
1092:
1080:
851:
835:
817:
801:
767:to its
690:
678:
540:SI unit
474:called
466:In the
436:to its
347:(e.g.,
293:degrees
289:radians
222:degrees
153:radians
62:Discuss
7471:
7438:. 2019
7386:
7312:
7232:GitHub
7095:"math"
6764:
6720:
6617:
6362:
6189:Series
5971:Circle
5967:Planes
5917:
5711:
5701:
5658:
5650:
5592:
5543:
5512:WP 34S
5322:
5276:
5237:
5094:
4980:
4969:– the
4903:1.47.0
4856:Python
4843:TWO_PI
4825:0.14.0
4762:Eiffel
4753:0.36.0
4685:period
4636:in ...
4621:Symbol
4588:(Hz),
3763:57.3°
3757:1 rad
3519:22.5°
3290:0 rad
3248:, 360
3208:radius
1722:sector
1502:rad =
1386:Notes
1378:Using
1372:Using
1332:τ
1293:Python
1285:τ
1277:τ
1263:τ
1209:τ
1187:π
1181:τ
1168:τ
1146:τ
1138:τ
1075:π
1071:τ
923:𝜏 = 2
769:radius
734:τ
676:), is
582:, and
564:newRPL
438:radius
359:and a
287:
276:circle
134:in ...
119:Symbol
58:merged
7597:Angle
7465:(PDF)
7395:(PDF)
7384:S2CID
7364:(PDF)
7339:(PDF)
7332:(PDF)
7310:S2CID
7292:arXiv
7066:"TAU"
6797:(PDF)
6790:(PDF)
6762:S2CID
6718:S2CID
6684:(PDF)
6677:(PDF)
6626:(PDF)
6615:S2CID
6589:(PDF)
6360:JSTOR
6281:(PDF)
6262:(PDF)
6204:'
5959:Areas
5957:, or
5818:ooPIC
5603:(PDF)
5586:(PDF)
5554:(PDF)
5537:(PDF)
5134:(PDF)
5123:(PDF)
5011:Notes
4942:Hertz
4924:2019
4921:0.6.0
4906:2020
4868:2016
4850:2013
4828:2016
4810:2022
4792:2018
4756:2021
4738:2020
4585:hertz
4513:(the
4259:360°
4238:270°
4196:turn
4173:180°
4146:turn
4123:144°
4081:turn
4041:120°
3999:turn
3935:turn
3870:turn
3789:turn
3769:63.7
3754:turn
3687:turn
3623:turn
3542:turn
3478:turn
3397:turn
3316:turn
3266:Turns
3230:6.283
2223:) = 2
2209:) = 1
1039:theta
936:1990)
860:Welsh
798:used
627:angle
530:]
492:below
490:(See
482:ratio
305:cycle
170:6.283
7469:ISBN
7410:OEIS
6509:"Pi"
6468:link
6443:E101
6394:E015
6330:E858
6274:E007
5915:ISBN
5709:LCCN
5699:ISBN
5656:OCLC
5648:LCCN
5590:ISBN
5541:ISBN
5320:ISBN
5274:ISBN
5235:ISSN
5092:ISBN
4894:Rust
4881:and
4874:Raku
4841:and
4798:Java
4729:and
4722:.NET
4582:are
4262:400
4256:rad
4241:300
4235:rad
4214:rad
4176:200
4170:rad
4164:rad
4126:160
4120:rad
4099:rad
4038:rad
4017:rad
3979:100
3976:90°
3973:rad
3953:rad
3912:72°
3909:rad
3888:rad
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