[Python] Can an arbitrary angle be trisected with a precision that surpasses any pratical...

The answer!

import mpmath as mp


# Set precision to 64-bit or higher
mp.mp.dps = 64 # Decimal places for precision

def trisect_angle(angle_degrees):
print(f"\nTrisecting angle: {angle_degrees} degrees")
angle_radians = mp.radians(angle_degrees)

# Quadrisect the angle
quadrisected_angle = angle_degrees / 4
C = mp.radians(quadrisected_angle)

# Lengths a and b (arbitrary but fixed values, can be adjusted)
a = b = 40

# Calculate the length of c using the law of cosines
c = mp.sqrt(a**2 + b**2 - 2 * a * b * mp.cos(C))
print(f"Length of c: {mp.nstr(c, 64)}")

# Calculate angle D in degrees using the law of cosines
f = g = 30
angleD_radians = mp.acos((f**2 + g**2 - c**2) / (2 * f * g))
angleD_degrees = mp.degrees(angleD_radians)
print(f"Angle D in degrees: {mp.nstr(angleD_degrees, 64)}")

# Calculate the small error in degrees outside the input angle
D3 = angleD_degrees * 3 - angle_degrees
print(f"Total error in degrees outside the input angle: {mp.nstr(D3, 64)}")

# Calculate angle E in degrees
angleE = D3 / 4
angleE_radians = mp.radians(angleE)
print(f"Angle E in degrees: {mp.nstr(angleE, 64)}")

# Calculate the length of e using the given formula
e = 2 * a * mp.sin(angleE_radians / 2)
print(f"Length of e: {mp.nstr(e, 64)}")

# Calculate angle H using the law of cosines
angleH_radians = mp.acos((f**2 + g**2 - e**2) / (2 * f * g))
angleH_degrees = mp.degrees(angleH_radians)
print(f"Angle H in degrees: {mp.nstr(angleH_degrees, 64)}")

# Calculate angle I as the difference between angle D and angle H
angleI_degrees = angleD_degrees - angleH_degrees
print(f"Angle I in degrees: {mp.nstr(angleI_degrees, 64)}")

# Calculate angle J = theta - 3 * I
angleJ = (angle_degrees - 3 * angleI_degrees) / 4
print(f"Angle J in degrees: {mp.nstr(angleJ, 64)}")

# Calculate the length of k using the given formula
angleJ_radians = mp.radians(angleJ)
k = 2 * a * mp.sin(angleJ_radians / 2)
print(f"Length of k: {mp.nstr(k, 64)}")

# Calculate angle L using the law of cosines
angleL_radians = mp.acos((f**2 + g**2 - k**2) / (2 * f * g))
angleL_degrees = mp.degrees(angleL_radians)
print(f"Angle L in degrees: {mp.nstr(angleL_degrees, 64)}")

# Calculate angle M as the sum of angle I and angle L
angleM_degrees = angleI_degrees + angleL_degrees
print(f"Angle M in degrees: {mp.nstr(angleM_degrees, 64)}")

return angleM_degrees

# Loop through angles from 100 to 360 in steps of 30
for angle in range(0, 361, 20):
trisect_angle(angle).



Please analyze my algorithm and give me your opinion. This algorithm trisects arbitrary angles with very high accuracy, precision and simplicity. You can adjust the angles you want to find the results for. Thanks in advance. Written in Python code and you will need to import mpmath as mp.The code sets the precision for the results.

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