三维自然螺旋解析-优快云博客

本文链接：https://blog.youkuaiyun.com/weixin_51095970/article/details/129217670

本文探讨了三维空间中的自然螺旋现象，结合numpy库和Python编程，深入解析其数学原理与实现方法，为机器学习领域的几何理解提供参考。

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三维自然螺旋

import numpy as np
#print(np.pi)
# r = sqrt([a/(πsin(θ/2))]e^θ)
a = 1
print("a = ",a)
li_temp = []
for i in range(60):
    li_temp.append((i+1)*2*np.pi/60)

m0 = 0
print("序号", ":", "锥角", " ", "斜长", " ", "面积")
for tha in li_temp:
    m0 +=1
    r = np.sqrt((a/(np.pi*np.sin(tha/2)))*(np.e**tha))
    s = a*(np.e**tha)
    print(m0, ":", tha, " ", r, " ", s)

# a =  1
# 序号 : 锥角   斜长   面积
# 1 : 0.10471975511965977   2.598750510857175   1.110399383005586
# 2 : 0.20943951023931953   1.9377020228037911   1.2329867897791864
# 3 : 0.3141592653589793   1.6690819504046392   1.369107770624847
# 4 : 0.41887902047863906   1.525611775259839   1.5202564237699834
# 5 : 0.5235987755982988   1.4408705930135899   1.6880917949644685
# 6 : 0.6283185307179586   1.3895414842023803   1.8744560875853382
# 7 : 0.7330382858376184   1.3596831765368407   2.0813948831258244
# 8 : 0.8377580409572781   1.3448853440332904   2.3111795940138995
# 9 : 0.9424777960769379   1.3413994820212334   2.566332395208135
# 10 : 1.0471975511965976   1.3469023804201457   2.849653908226361
# 11 : 1.1519173063162573   1.3598980349629455   3.164253941474008
# 12 : 1.2566370614359172   1.3794024460491732   3.5135856242857333
# 13 : 1.3613568165555772   1.4047661651912744   3.901483309344176
# 14 : 1.4660765716752369   1.435569089643079   4.332204659502365
# 15 : 1.5707963267948963   1.4715555162119789   4.81047738096535
# 16 : 1.6755160819145563   1.5125928004612903   5.341551115786253
# 17 : 1.7802358370342162   1.5586444830817097   5.931255063261856
# 18 : 1.8849555921538759   1.6097526455719746   6.586061962694724
# 19 : 1.9896753472735356   1.6660263829951831   7.313159139812781
# 20 : 2.0943951023931953   1.7276344906351666   8.120527396669774
# 21 : 2.199114857512855   1.7948011761694465   9.017028610942077
# 22 : 2.3038346126325147   1.8678040472817932   10.012503006133796
# 23 : 2.4085543677521746   1.9469739035333151   11.117877160352545
# 24 : 2.5132741228718345   2.032696046177218   12.345283939187366
# 25 : 2.6179938779914944   2.1254129483234423   13.708195669102425
# 26 : 2.7227136331111543   2.2256282232648306   15.221572013091183
# 27 : 2.827433388230814   2.333911905289888   16.902024171711542
# 28 : 2.9321531433504737   2.4509071246451137   18.767997211814002
# 29 : 3.0368728984701336   2.577338323643876   20.839972524248832
# 30 : 3.1415926535897927   2.714021230232742   23.140692632779253
# 31 : 3.2463124087094526   2.86187488437081   25.695410821759996
# 32 : 3.3510321638291125   3.021936107663114   28.532168322557368
# 33 : 3.4557519189487724   3.195376925486227   31.682102101179233
# 34 : 3.5604716740684323   3.3835256033421333   35.17978662546941
# 35 : 3.665191429188092   3.587892158976042   39.06361336318939
# 36 : 3.7699111843077517   3.810199477967534   43.376212176454274
# 37 : 3.8746309394274117   4.052421520393755   48.16491923785423
# 38 : 3.979350694547071   4.316830599694253   53.4822966042272
# 39 : 4.084070449666731   4.606056401361313   59.38670915105565
# 40 : 4.1887902047863905   4.923160378225161   65.94296520006436
# 41 : 4.29350995990605   5.271730548992192   73.22302787171029
# 42 : 4.39822971502571   5.6560037541376165   81.30680497054799
# 43 : 4.50294947014537   6.081025435944669   90.28302607345199
# 44 : 4.607669225265029   6.5528615780881285   100.2502164478383
# 45 : 4.71238898038469   7.078884525572517   111.31777848985618
# 46 : 4.817108735504349   7.668165672571244   123.60719255268877
# 47 : 4.9218284906240095   8.332026429989687   137.25335034555837
# 48 : 5.026548245743669   9.08482998117252   152.40603553915753
# 49 : 5.1312680008633285   9.945150743602701   169.2315678290079
# 50 : 5.235987755982989   10.93755768084153   187.91462850239847
# 51 : 5.340707511102648   12.095437508088342   208.66028754678715
# 52 : 5.445427266222309   13.465668550038615   231.69625454972075
# 53 : 5.550147021341968   15.116790533734546   257.2753780967151
# 54 : 5.654866776461628   17.154284167758217   285.6784211011212
# 55 : 5.759586531581288   19.751736022885947   317.2171425286952
# 56 : 5.8643062867009474   23.222209501137517   352.2377193426581
# 57 : 5.969026041820607   28.210863470306645   391.1245462293823
# 58 : 6.073745796940267   36.366786161307935   434.3044548114462
# 59 : 6.178465552059927   54.157889243641144   482.25139865920715
# 60 : 6.283185307179585   548505270.1110978   535.4916555247639