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Freeths Nephroid

Freeths Nephroid is a strophoid of a circle with the pole O at the centre of the circle and the fixed point P on the circumference of the circle.

Its polar equation is:

r = a (1 + 2 sin(theta / 2))

To plot function graph use the folowing script:

# Example
# 2D. Freeths Nephroid

# z must be zero
z = 0

# t-parameter
tmin = 0
tmax = 4*2*pi
tgrid = 400

# Constant
a = 2.5
n = 4

# Calculations
r = a * (1 + 2*sin(t/n))

x = r * cos(t)
y = r * sin(t)