Check out the newest video over on @RockHardWoodDaddy of the Series "Mathematics for Woodworkers" for full context! :) https://youtu.be/YLW7vmat5Og
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Python Code for the Real Life application: https://trinket.io/python/972253cc9e
Today we deal with a problem from my channel @RockHardWoodDaddy where we need to approximate a circle in the most efficient way using boards of wood, aka. rectangles. All of the generalization will lead us to spicy Riemann sums and an Integral in disguise. Enjoy! =D
Python Code:
import math
boards=int(input('Number of Boards? '))
diameter=int(input('Diameter of Table? '))
r=diameter/2
n=boards
A=0
if n%2==0:
for i in range(0, n // 2 + 1):
A += r * math.sqrt(1 - (2 * i / n) ** 2) * 2 * r / n
else:
for i in range(0,(n-1)//2+1):
A+=2*r**2/n*(math.sqrt(1-((2*i-1)/n)**2))
A+=2*r**2/n
print('Appr. Area is '+str(A*4))
print('Exact Area is '+str(math.pi * r**2))
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Want to know more about me? Watch my QnA! =D https://youtu.be/IjCWSDBI9Zc
0:00 What's the Problem?
3:15 n Even
7:53 n Odd
12:31 Generalization
17:48 Riemann Would Be Proud
25:35 Numerical Validation