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cut_the_circle.py
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cut_the_circle.py
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'''
Originally written by Jiaming Luo
For course "Mathematical Algorithm in Traditional Chinese Culture"
Finish date: December 13, 2019
Feel free to use or modify it
'''
from graphics import * #use "pip install graphics.py" if you don't have this library
import random
import time
from math import *
import numpy as np
class graph():
def __init__(self):
self.window = GraphWin("割圆术",900,700)
self.window.setCoords(-300,-350,600,350)
self.window.setBackground("gray")
self.center = Point(0,0)
self.radias = 250 #圆的半径
self.out_radias = 0 #外切正多边形距离圆心的距离
self.devide = 6 #正多边形的边数
self.inner_angle = [] #内接正多边形顶点的角度
self.outer_angle = [] #外切正多边形顶点的角度
self.inner_dots = [] #内接正多边形顶点的坐标
self.outer_dots = [] #外切正多边形顶点的坐标
self.inner_polygon = 0 #内接正多边形
self.outer_polygon = 0 #外切正多边形
self.inner_perimeter = 0 #内接正多边形周长
self.outer_perimeter = 0 #外切正多边形周长
self.txt_inner_p = Text(Point(430,200),"内接正多边形周长:")
self.txt_inner_p.setSize(15)
self.txt_inner_p.setTextColor("gold")
self.txt_inner_p.draw(self.window)
self.txt_outer_p = Text(Point(430,180),"外接正多边形周长:")
self.txt_outer_p.setSize(15)
self.txt_outer_p.setTextColor("DeepSkyBlue")
self.txt_outer_p.draw(self.window)
self.txt_circle_p = Text(Point(430,160),"圆的周长:"+str(round(2*pi,12)))
self.txt_circle_p.setSize(15)
self.txt_circle_p.setTextColor("crimson")
self.txt_circle_p.draw(self.window)
self.txt_pi_p = Text(Point(430,140),"PI的近似值:")
self.txt_pi_p.setSize(15)
self.txt_pi_p.setTextColor("PaleGreen")
self.txt_pi_p.draw(self.window)
self.explain = '''
说明:使用阿基米德方法进行圆周率PI的计算\n
首先输入正多边形的边数,点击“更新”按钮进行更新\n
可使用“自动进行”按钮让边长持续扩大两倍直到超过10万\n
自动进行可能有一些卡顿,等待结束后可重新操作\n
在非计算状态下可点击“退出”离开程序界面
'''
self.txt_pi_ex = Text(Point(420,-180),self.explain)
self.txt_pi_ex.setSize(12)
self.txt_pi_ex.setTextColor("Orange")
self.txt_pi_ex.draw(self.window)
self.init_draw()
self.run()
def init_draw(self):
self.circle = Circle(self.center,self.radias)
self.circle.setOutline("crimson")
self.circle.setWidth(2)
self.circle.draw(self.window)
self.devide_p = Point(450,60)
self.input1 = Entry(self.devide_p,5)
self.input1.setText(str(self.devide))
self.input1.setTextColor("white")
self.input1.draw(self.window)
t0=Text(Point(410,60),"边数:")
t0.setSize(12)
t0.draw(self.window)
self.btn_s = Rectangle(Point(390,-30),Point(430,10))
self.btn_s.setFill("white")
self.btn_s.setOutline("white")
self.btn_s.draw(self.window)
t1=Text(Point(410,-10),"更新").draw(self.window)
t1.setTextColor("black")
self.btn_e = Rectangle(Point(440,-30),Point(480,10))
self.btn_e.setFill("white")
self.btn_e.setOutline("white")
self.btn_e.draw(self.window)
t2=Text(Point(460,-10),"退出").draw(self.window)
t2.setTextColor("black")
self.btn_auto = Rectangle(Point(390,-80),Point(480,-40))
self.btn_auto.setFill("white")
self.btn_auto.setOutline("white")
self.btn_auto.draw(self.window)
t3=Text(Point(435,-60),"自动进行").draw(self.window)
t3.setTextColor("black")
def if_btn(self,point,btn): #判断鼠标点击是否在按钮内
ll = btn.getP1()
ur = btn.getP2()
return ll.getX() < point.getX() < ur.getX() and ll.getY() < point.getY() < ur.getY()
def draw_dot(self,dot,color = 'blue'): #画点
small_circle = Circle(dot,1)
small_circle.setOutline(color)
small_circle.setFill(color)
small_circle.draw(self.window)
return small_circle
def draw_polygon(self,point_list,color = 'green'): #画正多边形
p = Polygon(point_list)
p.setOutline(color)
p.setWidth(2)
p.draw(self.window)
return p
def dot_list_angle(self,devide): #获得n等分点的角度
return np.linspace(0,2*pi,devide,False).tolist()
def outer_radias(self,devide): #计算外切正多边形顶点与圆心的距离
angle = pi/devide
return self.radias/cos(angle)
def outer_dot_list_angle(self,devide): #获得外切正多边形的顶点角度
angle = pi/devide
return np.linspace(angle,2*pi+angle,devide,False).tolist()
def angle2point(self,radias,angle_list): #将角度转化成顶点坐标
point_list = []
for angle in angle_list:
point_list.append(Point(cos(angle)*radias,sin(angle)*radias))
return point_list
def perimeter(self,radias,devide): #计算正多边形的周长
angle = pi/devide
return round(devide*2*sin(angle)*radias/self.radias,11)
def draw_all(self): #更新所有显示内容
tmp = eval(self.input1.getText())
if tmp<=2 or type(tmp)!=int: #校验输入格式
pass
else:
self.devide = eval(self.input1.getText())
self.inner_angle = self.dot_list_angle(self.devide)
self.out_radias = self.outer_radias(self.devide)
self.outer_angle = self.outer_dot_list_angle(self.devide)
self.inner_dots = self.angle2point(self.radias,self.inner_angle)
self.outer_dots = self.angle2point(self.out_radias,self.outer_angle)
if self.inner_polygon!=0:
self.inner_polygon.undraw()
self.inner_polygon=self.draw_polygon(self.inner_dots,"gold")
if self.outer_polygon!=0:
self.outer_polygon.undraw()
self.outer_polygon=self.draw_polygon(self.outer_dots,"DeepSkyBlue")
self.inner_perimeter = self.perimeter(self.radias,self.devide)
self.outer_perimeter = self.perimeter(self.out_radias,self.devide)
self.txt_inner_p.undraw()
self.txt_inner_p = Text(Point(430,200),"内接正多边形周长:"+str(self.inner_perimeter))
self.txt_inner_p.setSize(15)
self.txt_inner_p.setTextColor("gold")
self.txt_inner_p.draw(self.window)
self.txt_outer_p.undraw()
self.txt_outer_p = Text(Point(430,180),"外接正多边形周长:"+str(self.outer_perimeter))
self.txt_outer_p.setSize(15)
self.txt_outer_p.setTextColor("DeepSkyBlue")
self.txt_outer_p.draw(self.window)
self.txt_pi_p.undraw()
self.txt_pi_p = Text(Point(430,140),"PI的近似值:"+str(round(((self.inner_perimeter+self.outer_perimeter)/4),11)))
self.txt_pi_p.setSize(15)
self.txt_pi_p.setTextColor("PaleGreen")
self.txt_pi_p.draw(self.window)
def run(self):
while True:
self.draw_all()
point = self.window.getMouse()
if self.if_btn(point,self.btn_s): #更新
self.draw_all()
if self.if_btn(point,self.btn_e): #退出
break
if self.if_btn(point,self.btn_auto): #自动播放
while self.devide <=100000: #一直加倍直到100,000(这个值可以修改)
self.input1.setText(str(self.devide*2))
time.sleep(.5)
self.draw_all()
self.window.close()
if __name__ == "__main__":
graph = graph()