- БРОЈ ПИ
Постоји пуно образаца за број Пи.,можете их погледати [1]
Број Пи нема само круг већ читав низ геометријских слика почев троугао,четвороугао, петоугао итд
2004 год. Пронашао сам јединствени образац за све ПИ бројеве:
![{\displaystyle \pi _{n}={\frac {n}{2}}.sin({\frac {360}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f9f12977d529090434de1e7f8d26a5542f5b3b1f)
Постоје два решења зависно како рачунамо синус 1)за синус у степенима добиће се Пи 2)за синус у радијанима добија се 180 ова особина новог обрасца је иста као и код старих тригонометријских образаца за број Пи али обратно.Мисли се на ПИ круга.
- n= {3,4,5,6........., бесконачно}
- n=3 ради се о једнакостраничном троуглу
![{\displaystyle \pi _{3}={\frac {3}{2}}\sin({\frac {360}{3}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/750ec6bb057096185dad61319ce882eb07cade0d)
![{\displaystyle \pi _{3}=1.299038105676657970145584756129404275207103940357785471041855234588949762681600027810859640067936431756719606061555027272477458821249214359108741634070780236396069923926729186550981115075813506192448761484257450177492164988004191001691378478420285348745275896191014287489903034894542100737760629932038067463761097204575710701640392743812359372142969874748342368381216535847874688010418122988440891548250968547863765249583132380335670783737076566229143676252517640533358216521993217274347815376373554674619972363212265589806452991554023153186737988373546994737255879027157790435027172484077780448014436830076173399466281730856066512557064076779745703123294923844606990748216673347110878468792671641139677682025389606048286479258495794767292154648948115366998523815015896613116458830885964900880276393737512516970811610634553457857999822195125972183078771421332595361479060232409486838841413231534260410498721433971667217832916432192792394148303696921223601631524640287512203987208937787304127.......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f64776b69c55b713389e86b62bf9afed44559068)
Површина једнакостраничног троугла биће
![{\displaystyle R^{2}\pi _{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9655bc17e109833eadacb7fa3a05f5812cec01c8)
R -Полупречник описане кружнице око једнакостраничног троугла
- Обим једнакостраничног троугла биће
![{\displaystyle O={\frac {2R\pi _{3}}{\cos {\frac {\alpha }{2}}}}:\alpha ={\frac {360}{3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/577fd10fc2b3dcc22c5923a547e8fa6063cd582d)
- n=4 ради се о квадрату
![{\displaystyle \pi _{4}=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/85b70f9beecc8f721abfda3d1650dde00db3f106)
Површина квадрата биће
![{\displaystyle R^{2}\pi _{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d5a48e0eb0f0f8f260ca51c150a74c53172593f)
R -Полупречник описане кружнице око квадрата
- Обим квадрата биће
![{\displaystyle O={\frac {2R\pi _{4}}{\cos {\frac {\alpha }{2}}}}:\alpha ={\frac {360}{4}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/62cee1c06ce9615690425a398bc087edb897197a)
тако даље петоугао,шестоугао .......
![{\displaystyle \pi _{5}=2.37764129073788393029109833344845535851424658531437555611826411107538292521298375429698202742702845418974929387850751052246766548442424981578803067578295594696444359492600258179554275230250379513151001423802924795917183008219605036301495148507880140322781045987090044531881885084349467130129921084258543849815492459549445122232219143670592470372285079329288667825627445956811065730153458201304781755172126659167760259062780734991737248477967564240583159502841310815397363785669533897013826055892072659996199853464482719029151537061472938008846993548889178745205678459542206169347872570742004980802724766701370391337077603044283323962631433827549038847681729685293628396669902392009519093871640782190843048473742646406880592139994355352920382189607783603508041226848456648980006775286567800517085352418736253370309354164490169821718538097751802464867296154739841155499816959251406543633373361369339814369337895730123108013172623915093695955211484250762466097770012856809360256952109203831071625}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7d00fb4ec8d216e6f80d53fedcd26e6df74f073)
![{\displaystyle \pi _{6}=2.59807621135331594029116951225880855041420788071557094208371046917789952536320005562171928013587286351343921212311005454495491764249842871821748326814156047279213984785345837310196223015162701238489752296851490035498432997600838200338275695684057069749055179238202857497980606978908420147552125986407613492752219440915142140328078548762471874428593974949668473676243307169574937602083624597688178309650193709572753049916626476067134156747415313245828735250503528106671643304398643454869563075274710934923994472642453117961290598310804630637347597674709398947451175805431558087005434496815556089602887366015234679893256346171213302511412815355949140624658984768921398149643334669422175693758534328227935536405077921209657295851699158953458430929789623073399704763003179322623291766177192980176055278747502503394162322126910691571599964439025194436615754284266519072295812046481897367768282646306852082099744286794333443566583286438558478829660739384244720326304928057502440797441787557460825459}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2061637f7c19e9949aac2ee0c4ea4174ba31f637)
- доказ
![{\displaystyle \pi ={\frac {n}{2}}.sin({\frac {360}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/721c663a8b03abc7a7ab5e5d3657fc26e0ebc7c9)
![{\displaystyle lim_{n\to \infty }{\frac {n}{2}}.sin({\frac {360}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adba26537af19ef38ca989b3065f8aec3eb2e917)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }n.sin({\frac {360}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/58adaf73986d923038c6b9ebcf50ab308fb184d9)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {360}{n}})}{\frac {1}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/16a5c87b7c1c30d908fe7fd4486d50ecc4f64863)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {360}{n}})}{\frac {1}{n}}}.{\frac {360}{360}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e1a3ae7c4110eb3b9e71ffd8b6218bc1f2ebbdf)
![{\displaystyle {\frac {360}{2}}lim_{n\to \infty }{\frac {sin({\frac {360}{n}})}{\frac {360}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a750d37d7683bd3be2e6f17018e7f1f1124346f)
![{\displaystyle {\frac {360}{n}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/561959107f30bcb21f821397074a0fe02a411ff3)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 180\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=180^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e66394adccc07581e7aa1d49c60c8acea07324)
![{\displaystyle 180^{0}=\pi (rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1429cffef3ca9ec6bec04275728017db81a7d6)
- -------------------------------------------------------
Још један образац 2004 год
- Иста особина обрасца како је већ речено за синус (степени,радијани)
![{\displaystyle \pi =180.m.sin({\frac {1}{m}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05af6bca0f6b669f3136c1d63d8f5677bf6c1cd1)
![{\displaystyle \lim _{m\to \infty }180.m.sin({\frac {1}{m}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9da439941386d9777f6bf5ab525e883f271dca1a)
![{\displaystyle 180\lim _{m\to \infty }m.sin({\frac {1}{m}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b69747ef01fea0f20aa616cd2fa0771d2b0d6a16)
![{\displaystyle 180\lim _{m\to \infty }{\frac {sin({\frac {1}{m}})}{\frac {1}{m}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae629ba1fc84e297cddbf57719c86c0ba223066)
![{\displaystyle {\frac {1}{m}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/296e73a544fd87af4454d4fb60b96963bf21a4b7)
![{\displaystyle m\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3973cdef1dfd8669d3320e5bef4a2e146802f5a7)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 180\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=180^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e66394adccc07581e7aa1d49c60c8acea07324)
![{\displaystyle 180^{0}=\pi (rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1429cffef3ca9ec6bec04275728017db81a7d6)
- -------------------------------------------------------
биће
![{\displaystyle {\frac {\pi }{2}}={\frac {n}{2}}sin({\frac {180}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/067dff59e7522e24d25d4d1f2a21893ddaa6b971)
- доказ
![{\displaystyle lim_{n\to \infty }{\frac {n}{2}}.sin({\frac {180}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/45b8b32ed3469e5168cdce8a6fea0de121bd2db6)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }n.sin({\frac {180}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/58fa4fac25c4585d9f6a4f786e6419985be12114)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {180}{n}})}{\frac {1}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/159da4d900c1e6724a9fd9d58a975eec770ae693)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {180}{n}})}{\frac {1}{n}}}.{\frac {180}{180}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e98dcc1b2aacae0424e43594cd2b009dadeb0a4f)
![{\displaystyle 90\lim _{m\to \infty }{\frac {sin({\frac {1}{m}})}{\frac {1}{m}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/40fe02e7d2689fb52088b091ede75b7cae746ac5)
![{\displaystyle {\frac {180}{n}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43957d78ad0b55b607cc2abfc21215c5a89628a9)
![{\displaystyle n\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d55d9b32f6fa8fab6a84ea444a6b5a24bb45e1)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 90\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=90^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/926b8ba4db9643517e75214718506f84fb57bb7f)
![{\displaystyle 90^{0}={\frac {\pi }{2}}(rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f80581ad2566eb376f186ba7552db6a0f4e7a003)
- -------------------------------------------------------
биће
![{\displaystyle {\frac {\pi }{3}}={\frac {n}{2}}sin({\frac {120}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26836faa53fe4c410213d89bef18b4d61ea8b10e)
- доказ
![{\displaystyle lim_{n\to \infty }{\frac {n}{2}}.sin({\frac {120}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f8f7c94801d69805da67d15ff1c60519b9d5862e)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }n.sin({\frac {120}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61b768355c9d65171b56b06a5de5afd6db6cac49)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {120}{n}})}{\frac {1}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e600fd9376304ebd2c1a98fd7f1499159723b82e)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {120}{n}})}{\frac {1}{n}}}.{\frac {120}{120}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/82eade727ca17d6400e74fdb081a091fd6dc0e31)
![{\displaystyle 60\lim _{n\to \infty }{\frac {sin({\frac {120}{n}})}{\frac {120}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe864e968da85316b4811795a0bc6ebfb036419)
![{\displaystyle {\frac {120}{n}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e7d4a8ea2430deffbce9f5116a891f037798de8)
![{\displaystyle n\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d55d9b32f6fa8fab6a84ea444a6b5a24bb45e1)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 60\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=60^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c297365bffea54f77c98a014c15e46cd6768090)
![{\displaystyle 60^{0}={\frac {\pi }{3}}(rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0422a23286ab75ae9a8bf01725df3929f1f65522)
- -------------------------------------------------------
биће
![{\displaystyle {\frac {\pi }{4}}={\frac {n}{2}}.sin({\frac {90}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9de4dd5f392eeacdcc7c2d5f4f5b241146d3cf88)
- доказ
![{\displaystyle lim_{n\to \infty }{\frac {n}{2}}.sin({\frac {90}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6c6e08cb6e1c445246b64edb1a0a3ede15e6394)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }n.sin({\frac {90}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aab5f09ba30a275330dd8ff000ffd76bc1f63c4d)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {90}{n}})}{\frac {1}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0d72e6bf6f5449436479ac811a262ed24debc2)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {90}{n}})}{\frac {1}{n}}}.{\frac {90}{90}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c0ed81093f1f87203a6469ad9d65798d99a5f63)
![{\displaystyle {\frac {90}{2}}lim_{n\to \infty }{\frac {sin({\frac {90}{n}})}{\frac {90}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53177380a59155fcf9fcc7c92fd78fa10b0c1a77)
![{\displaystyle {\frac {90}{n}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1d17855dcde84cccc038e4e00b86aeeb04a0ea9)
![{\displaystyle n\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d55d9b32f6fa8fab6a84ea444a6b5a24bb45e1)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 45\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=45^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56a9e0a86365204dc212ab743a4b17827291f7f2)
![{\displaystyle 45^{0}={\frac {\pi }{4}}(rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/879db0e1b696b9fe321707be5c0626ea1c6c5561)
- -------------------------------------------------------
биће
![{\displaystyle {\frac {\pi }{5}}={\frac {n}{2}}sin({\frac {72}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05571afbddde586b5b3051a84afb2202f0f67dea)
- доказ
![{\displaystyle lim_{n\to \infty }{\frac {n}{2}}.sin({\frac {72}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f7bab79c8c81cbbf604c8ecd282f3c7dc1d17ed)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }n.sin({\frac {72}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/840e581ccdee985b12b2908fb4fbcf5db03c68dc)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {72}{n}})}{\frac {1}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e18a71a4491b75ff9a59b7b6801f4865805c25ff)
![{\displaystyle {\frac {1}{2}}lim_{n\to \infty }{\frac {sin({\frac {72}{n}})}{\frac {1}{n}}}.{\frac {72}{72}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13ed75ecd4217fa7ab9c0f22b8940aa7f501e8c3)
![{\displaystyle {\frac {72}{2}}lim_{n\to \infty }{\frac {sin({\frac {72}{n}})}{\frac {72}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91f2c5649101b66b031d61f35c316b0e3e2c5bc1)
![{\displaystyle {\frac {72}{n}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aced43a77c1142b770cc935ee3cb4cb986ca2085)
![{\displaystyle n\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d55d9b32f6fa8fab6a84ea444a6b5a24bb45e1)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle {\frac {72}{2}}lim_{t\to \mathbf {0} }{\frac {sint}{t}}={\frac {72}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7b5106c0cb7f56c7c6977685c9b25d5ca53bd5e)
![{\displaystyle {\frac {72}{2}}={\frac {\pi }{5}}(rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b66b8e32b66786eeee925d82f6c555db5a196420)
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биће
![{\displaystyle {\frac {\pi }{8}}={\frac {n}{2}}sin({\frac {45}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0ef0573eff6fd84b5494ef4ff98c795ab122c9)
- итд
- -------------------------------------------------------
Још један образац 2004 год
већ је речено степени,радијани
![{\displaystyle \pi =n.\sin({\frac {180}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f56fb195717b38493128ba4df07b00b2a7c9555f)
- доказ
![{\displaystyle \ lim_{n\to \infty }n.sin({\frac {180}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f994d88eb1e5f8ab129f9a7c44646f06ba5500d)
![{\displaystyle \ lim_{n\to \infty }{\frac {sin({\frac {180}{n}})}{\frac {1}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24d48d42c0442a159dec68eda0d8349c1b475aa6)
![{\displaystyle \ lim_{n\to \infty }{\frac {sin({\frac {180}{n}})}{\frac {1}{n}}}.{\frac {180}{180}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b5d9fa094184f39784f7a5ae8497e04b8c74c03a)
![{\displaystyle 180\lim _{m\to \infty }{\frac {sin({\frac {180}{n}})}{\frac {180}{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f6e2253f756ea842aecb2e177c10f4be33f9a6)
![{\displaystyle {\frac {180}{n}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43957d78ad0b55b607cc2abfc21215c5a89628a9)
![{\displaystyle n\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d55d9b32f6fa8fab6a84ea444a6b5a24bb45e1)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 180\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=180^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e66394adccc07581e7aa1d49c60c8acea07324)
![{\displaystyle 180^{0}=\pi (rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1429cffef3ca9ec6bec04275728017db81a7d6)
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биће
![{\displaystyle {\frac {\pi }{2}}=n.\sin({\frac {90}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4967e9a54357489b4aac963ce024b59cb50b9692)
постоји гранична вредност
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биће
![{\displaystyle {\frac {\pi }{3}}=n.\sin({\frac {60}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4723b3c4fe47a2d0bea150604dfe3b515b332a8d)
такође постоји гранична вредност
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прескачемо
биће
![{\displaystyle {\frac {\pi }{5}}=n.\sin({\frac {36}{n}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/541ed2ae6d71bdd8534244edd311b4b7d2d68317)
- има граничну вредност
- итд
Још један образац 2004 год
већ је речено степени,радијани
![{\displaystyle \pi =360.m.sin({\frac {1}{2m}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f467e4b1c00c33cdc74d8cad4d7212f0a999bef)
![{\displaystyle \lim _{m\to \infty }360.m.sin({\frac {1}{2m}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76b0486208177955dfacb3527998f5baedd26ff1)
![{\displaystyle 360\lim _{m\to \infty }m.sin({\frac {1}{2m}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0cd2f194329e21a813e50b47aa589b96b2ca247)
![{\displaystyle 360\lim _{m\to \infty }{\frac {sin({\frac {1}{2m}})}{\frac {1}{m}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/710784276ba65f4c67593949f6c8849e0dad453e)
![{\displaystyle 360\lim _{m\to \infty }{\frac {sin({\frac {1}{2m}})}{\frac {1}{m}}}{\frac {\frac {1}{2}}{\frac {1}{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c07394bec3d52e3a98cf1b91ad40bb76dcb5381c)
![{\displaystyle 360.{\frac {1}{2}}\lim _{m\to \infty }{\frac {sin({\frac {1}{2m}})}{\frac {1}{2m}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80f0098e38924cb76541112051c0bfba300f30da)
![{\displaystyle {\frac {1}{2m}}=t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4e711bddddb7d1167f8d00a10ab93265de97f16)
![{\displaystyle m\to \infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3973cdef1dfd8669d3320e5bef4a2e146802f5a7)
![{\displaystyle t\rightarrow \ 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1724e1aac77e58d966afa79a090b28a2723d997c)
![{\displaystyle 180\lim _{t\to \mathbf {0} }{\frac {sint}{t}}=180^{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e66394adccc07581e7aa1d49c60c8acea07324)
![{\displaystyle 180^{0}=\pi (rad)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1429cffef3ca9ec6bec04275728017db81a7d6)
За нумеричке вредности препоручујем калкулатор extra precision calculator Harry-J-Smith XP,XM,
Споменице и захвалнице су део примитиваца
(Рајко Велимировић (разговор) 07:20, 21. децембар 2011. (CET))