院系:李煌數學研究院/正多邊形內角大小(精確值)

正多邊形內角大小,指正多邊形每個內角大小,內角大小可以有三種情況包括整數、有限小數和無限循環小數。

角度與弧度轉換

角度	弧度
180°	pi
360°	2 * pi
120°	2/3 * pi
240°	4/3 * pi
360°	2 * pi
90°	1/2 * pi
180°	pi
270°	3/2 * pi
360°	2 * pi
72°	2/5 * pi
144°	4/5 * pi
216°	6/5 * pi
288°	8/5 * pi
360°	2 * pi
60°	1/3 * pi
120°	2/3 * pi
180°	pi
240°	4/3 * pi
300°	5/3 * pi
360°	2 * pi
45°	1/4 * pi
90°	1/2 * pi
135°	3/4 * pi
180°	pi
225°	5/4 * pi
270°	3/2 * pi
315°	7/4 * pi
360°	2 * pi

邊數(3-20)

邊數	每個內角大小
3	60°
4	90°
5	108°
6	120°
7	128.(571428)°
8	135°
9	140°
10	144°
11	147.(27)°
12	150°
13	152.(307692)°
14	154.(285714)°
15	156°
16	157.5°
17	158.(8235294117647058)°
18	160°
19	161.(052631578947368421)°
20	162°

邊數(200以內)

邊數	每個內角大小
3	60°
4	90°
5	108°
6	120°
8	135°
9	140°
10	144°
12	150°
15	156°
16	157.5°
18	160°
20	162°
24	165°
25	165.6°
30	168°
32	168.75°
36	170°
40	171°
45	172°
48	172.5°
50	172.8°
60	174°
64	174.375°
72	175°
75	175.2°
80	175.5°
90	176°
96	176.25°
100	176.4°
120	177°
125	177.12°
128	177.1875°
144	177.5°
150	177.6°
160	177.75°
180	178°
192	178.125°
200	178.2°

邊數(201-500)

邊數	每個內角大小
225	178.4°
240	178.5°
250	178.56°
256	178.59375°
288	178.75°
300	178.8°
320	178.875°
360	179°
375	179.04°
384	179.0625°
400	179.1°
450	179.2°
480	179.25°
500	179.28°

邊數(4x2^n)

邊數	每個內角大小
4	90°
8	135°
16	157.5°
32	168.75°
64	174.375°
128	177.1875°
256	178.59375°
512	179.296875°
1024	179.6484375°
2048	179.82421875°
4096	179.912109375°
8192	179.9560546875°
16384	179.97802734375°
32768	179.989013671875°
65536	179.9945068359375°
131072	179.99725341796875°
262144	179.998626708984375°
524288	179.9993133544921875°
1048576	179.99965667724609375°
2097152	179.999828338623046875°
4194304	179.9999141693115234375°
8388608	179.99995708465576171875°
16777216	179.999978542327880859375°
33554432	179.9999892711639404296875°
67108864	179.99999463558197021484375°
134217728	179.999997317790985107421875°
268435456	179.9999986588954925537109375°
536870912	179.99999932944774627685546875°
1073741824	179.999999664723873138427734375°
2147483648	179.9999998323619365692138671875°
4294967296	179.99999991618096828460693359375°
8589934592	179.999999958090484142303466796875°
17179869184	179.9999999790452420711517333984375°
34359738368	179.99999998952262103557586669921875°
68719476736	179.999999994761310517787933349609375°
137438953472	179.9999999973806552588939666748046875°
274877906944	179.99999999869032762944698333740234375°
549755813888	179.999999999345163814723491668701171875°
1099511627776	179.9999999996725819073617458343505859375°
2199023255552	179.99999999983629095368087291717529296875°
4398046511104	179.999999999918145476840436458587646484375°
8796093022208	179.9999999999590727384202182292938232421875°
17592186044416	179.99999999997953636921010911464691162109375°
35184372088832	179.999999999989768184605054557323455810546875°
70368744177664	179.9999999999948840923025272786617279052734375°
140737488355328	179.99999999999744204615126363933086395263671875°
281474976710656	179.999999999998721023075631819665431976318359375°
562949953421312	179.9999999999993605115378159098327159881591796875°
1125899906842624	179.99999999999968025576890795491635799407958984375°
2251799813685248	179.999999999999840127884453977458178997039794921875°
4503599627370496	179.9999999999999200639422269887290894985198974609375°
9007199254740992	179.99999999999996003197111349436454474925994837046875°

邊數(5x2^n)

邊數	每個內角大小
5	108°
10	144°
20	162°
40	171°
80	175.5°
160	177.75°
320	178.875°
640	179.4375°
1280	179.71875°
2560	179.859375°
5120	179.9296875°
10240	179.96484375°
20480	179.982421875°
40960	179.9912109375°
81920	179.99560546875°
163840	179.997802734375°
327680	179.9989013671875°
655360	179.99945068359375°
1310720	179.999725341796875°
2621440	179.9998626708984375°
5242880	179.99993133544921875°
10485760	179.999965667724609375°
20971520	179.9999828338623046875°
41943040	179.99999141693115234375°
83886080	179.999995708465576171875°
167772160	179.9999978542327880859375°
335544320	179.99999892711639404296875°
671088640	179.999999463558197021484375°
1342177280	179.9999997317790985107421875°
2684354560	179.99999986588954925537109375°
5368709120	179.999999932944774627685546875°
10737418240	179.9999999664723873138427734375°
21474836480	179.99999998323619365692138671875°
42949672960	179.999999991618096828460693359375°
85899345920	179.9999999958090484142303466796875°
171798691840	179.99999999790452420711517333984375°
343597383680	179.999999998952262103557586669921875°
687194767360	179.9999999994761310517787933349609375°
1374389534720	179.99999999973806552588939666748046875°
2748779069440	179.999999999869032762944698333740234375°
5497558138880	179.9999999999345163814723491668701171875°

邊數(3x2^n)

邊數	每個內角大小
3	60°
6	120°
12	150°
24	165°
48	172.5°
96	176.25°
192	178.125°
384	179.0625°
768	179.53125°
1536	179.765625°
3072	179.8828125°
6144	179.94140625°
12288	179.970703125°
24576	179.9853515625°
49152	179.99267578125°
98304	179.996337890625°
196608	179.9981689453125°
393216	179.99908447265625°
786432	179.999542236328125°
1572864	179.9997711181640625°
3145728	179.99988555908203125°
6291456	179.999942779541015625°
12582912	179.9999713897705078125°
25165824	179.99998569488525390625°
50331648	179.999992847442626953125°
100663296	179.9999964237213134765625°
201326592	179.99999821186065673828125°
402653184	179.999999105930328369140625°
805306368	179.9999995529651641845703125°
1610612736	179.99999977648258209228515625°
3221225472	179.999999888241291046142578125°
6442450944	179.9999999441206455230712890625°
12884901888	179.99999997206032276153564453125°
25769803776	179.999999986030161380767822265625°
51539607552	179.9999999930150806903839111328125°
103079215104	179.99999999650754034519195556640625°
206158430208	179.999999998253770172595977783203125°
412316860416	179.9999999991268850862979888916015625°
824633720832	179.99999999956344254314899444580078125°
1649267441664	179.999999999781721271574497222900390625°
3298534883328	179.9999999998908606357872486114501953125°
6597069766656	179.99999999994543031789362430572509765625°
13194139533312	179.999999999972715158946812152862548828125°
26388279066624	179.9999999999863575794734060764312744140625°
52776558133248	179.99999999999317878973670303821563720703125°
105553116266496	179.999999999996589394868351519107818603515625°
211106232532992	179.9999999999982946974371757595539093017578125°
422212465065984	179.99999999999914734871708787977695465087890625°
844424930131968	179.999999999999573674358543939888477325439453125°

邊數(9x2^n)

邊數	每個內角大小
9	140°
18	160°
36	170°
72	175°
144	177.5°
288	178.75°
576	179.375°
1152	179.6875°
2304	179.84375°
4608	179.921875°
9216	179.9609375°
18432	179.98046875°
36864	179.990234375°
73728	179.9951171875°
147456	179.99755859375°
294912	179.998779296875°
589824	179.9993896484375°
1179648	179.99969482421875°
2359296	179.999847412109375°
4718592	179.9999237060546875°
9437184	179.99996185302734375°
18874368	179.999980926513671875°
37748736	179.9999904632568359375°
75497472	179.99999523162841796875°
150994944	179.999997615814208984375°
301989888	179.9999988079071044921875°
603979776	179.99999940395355224609375°
1207959552	179.999999701976776123046875°
2415919104	179.9999998509883880615234375°
4831838208	179.99999992549419403076171875°
9663676416	179.999999962747097015380859375°
19327352832	179.9999999813735485076904296875°
38654705664	179.99999999068677425384521484375°
77309411328	179.999999995343387126922607421875°
154618822656	179.9999999976716935634613037109375°
309237645312	179.99999999883584678173065185546875°
618475290624	179.999999999417923390865325927734375°
1236950581248	179.9999999997089616954326629638671875°
2473901162496	179.99999999985448084771633148193359375°
4947802324992	179.999999999927240423858165740966796875°
9895604649984	179.9999999999636202119290828704833984375°
19791209299968	179.99999999998181010596454143524169921875°
39582418599936	179.999999999990905052982270717620849069375°
79164837199872	179.9999999999954525264911353588104248046875°

邊數(5^n)

邊數	每個內角大小
5	108°
25	156.6°
125	177.12°
625	179.424°
3125	179.8848°
15625	179.97696°
78125	179.995392°
390625	179.9990784°
1953125	179.99981568°
9765625	179.999963136°
48828125	179.9999926272°
244140625	179.99999852544°
1220703125	179.999999705088°
6103515625	179.9999999410176°
30517578125	179.99999998820352°
152587890625	179.999999997640704°
762939453125	179.9999999995281408°
3814697265625	179.99999999990562816°
19073486328125	179.999999999981125632°
95367431640625	179.9999999999962251264°
476837158203125	179.99999999999924502528°
2384185791015625	179.999999999999849005056°
11920928955078125	179.9999999999999689010112°
59604644775390625	179.99999999999999396020224°
298023223876953125	179.999999999999998792040448°
1490116119384765625	179.9999999999999997584080896°
7450580596923828125	179.99999999999999995168161792°
37252902984619140625	179.999999999999999990336323584°
186264514923095703125	179.9999999999999999980672647168°
931322574615478515625	179.99999999999999999961345294336°
4656612873077392578125	179.999999999999999999922690588672°
23283064365386962890625	179.9999999999999999999845381177344°
116415321826934814453125	179.99999999999999999999690762354688°
582076609134674072265625	179.999999999999999999999381524709376°
2910383045673370361328125	179.9999999999999999999998763049418752°
14551915228366851806640625	179.99999999999999999999997526098837504°
72759576141834259033203125	179.999999999999999999999995052197675008°
363797880709171295166015625	179.9999999999999999999999990104395350016°
1818989403545856475830078125	179.99999999999999999999999980208790700032°
9094947017729282379150390625	179.999999999999999999999999960417581400064°
45474735088646411895751953125	179.9999999999999999999999999920835162800128°
227373675443232059478759765625	179.99999999999999999999999999841670325600256°
1136868377216160297393798828125	179.999999999999999999999999999683340651200512°
5684341886080801486968994140625	179.9999999999999999999999999999366681302401024°
28421709430404007434844970703125	179.99999999999999999999999999998733362604802048°
142108547152020037174224853515625	179.999999999999999999999999999997466725209604096°
710542735760100185871124267578125	179.9999999999999999999999999999994933450419208192°

邊數(2x5^n)

邊數	每個內角大小
10	144°
50	172.8°
250	178.56°
1250	179.712°
6250	179.9424°
31250	179.98848°
156250	179.997696°
781250	179.9995392°
3906250	179.99990784°
19531250	179.999981568°
97656250	179.9999963136°
488281250	179.99999926272°
2441406250	179.999999852544°
12207031250	179.9999999705088°
61035156250	179.99999999410176°
305175781250	179.999999998820352°
1525878906250	179.9999999997640704°
7629394531250	179.99999999995281408°
38146972656250	179.999999999990562816°
190734863281250	179.9999999999981125632°
953674316406250	179.99999999999962251264°
4768371582031250	179.999999999999924502528°
23841857910156250	179.9999999999999849005056°
119209289550781250	179.99999999999999689010112°
596046447753906250	179.999999999999999396020224°
2980232238769531250	179.9999999999999998792040448°
14901161193847656250	179.99999999999999997584080896°
74505805969238281250	179.999999999999999995168161792°
372529029846191406250	179.9999999999999999990336323584°
1862645149230957031250	179.99999999999999999980672647168°
9313225746154785156250	179.999999999999999999961345294336°

邊數(10^n)

邊數	每個內角大小
10	144°
100	176.4°
1000	179.64°
10000	179.964°
100000	179.9964°
1000000	179.99964°
10000000	179.999964°
100000000	179.9999964°
1000000000	179.99999964°
10000000000	179.999999964°
100000000000	179.9999999964°
1000000000000	179.99999999964°
10000000000000	179.999999999964°
100000000000000	179.9999999999964°
1000000000000000	179.99999999999964°
10000000000000000	179.999999999999964°
100000000000000000	179.9999999999999964°
1000000000000000000	179.99999999999999964°
10000000000000000000	179.999999999999999964°
100000000000000000000	179.9999999999999999964°
1000000000000000000000	179.99999999999999999964°
10000000000000000000000	179.999999999999999999964°
100000000000000000000000	179.9999999999999999999964°
1000000000000000000000000	179.99999999999999999999964°

邊數(36x10^n)

邊數	每個內角大小
36	170°
360	179°
3600	179.9°
36000	179.99°
360000	179.999°
3600000	179.9999°
36000000	179.99999°
360000000	179.999999°
3600000000	179.9999999°
36000000000	179.99999999°
360000000000	179.999999999°
3600000000000	179.9999999999°
36000000000000	179.99999999999°
360000000000000	179.999999999999°
3600000000000000	179.9999999999999°
36000000000000000	179.99999999999999°
360000000000000000	179.999999999999999°
3600000000000000000	179.9999999999999999°
36000000000000000000	179.99999999999999999°
360000000000000000000	179.999999999999999999°
3600000000000000000000	179.9999999999999999999°
36000000000000000000000	179.99999999999999999999°
360000000000000000000000	179.999999999999999999999°