Setup

import math
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from random import choice as RC
from random import random as RR
import seaborn as sns

#Get a random point on sandwich edge.
def getPoint() :
    #Randomly select x or y axis.
    s = RC(("x","y"))
    #Randomly select corresponding left/right or down/up.
    v = RC((0, 1))
    
    if s == "x":
        x = v
        y = RR()
    
    else:
        x = RR()
        y = v
    return((x, y))

#Get the smaller sandwich piece's area.
def getSmallerArea(p) :
    x_0 = RR()
    y_0 = 0
    x_1 = p[0]
    y_1 = p[1]
    
    #1/4 of points will be on the same side.  Still one square. A = 0.
    if y_1 == 0 :
        A = 0
    
    #1/2 of points will be on adjacent sides. One triangle, one pentagon, determine area of triangle (always smaller).
    elif x_1 == 0 or x_1 == 1 :
        if x_1 == 0 :
            A = x_0 * y_1 / 2
        else :
            A = (1-x_0) * y_1 / 2

    #1/4 of points will be on opposite sides. Two trapezoids. determine which one is smaller.
    else : #y_1 == 1
        
        #Left trapezoid
        a_left = (x_0 + x_1) / 2 
        
        #Right trapezoid
        a_right = ((1-x_0) + (1-x_1)) / 2
        
        if a_left < a_right :
            A = a_left
        else :
            A = a_right
    
    return(A)

areas = []
for i in range(100000000):
    A = getSmallerArea(getPoint())
    areas.append(A)

total = 0
for a in areas:
    if a >= 0.25:
        total += 1

print( total)

26423527

7/16 + 0.25*math.log(0.5)

0.26421320486001365

Rohan Lewis

2022.11.14