File:Nodary.svg

Summary[edit]

Creation[edit]

The parameterization used was

${\displaystyle x=a\left(1-\cos u+\int \limits _{0}^{u}{\frac {\sin ^{2}\alpha }{\sqrt {\sin ^{2}\alpha +\beta }}}d\alpha \right)}$

${\displaystyle y=a(\sin u+{\sqrt {\sin ^{2}u+\beta }})}$

with ${\displaystyle \beta =a^{2}/b^{2}}$ where ${\displaystyle a}$ and ${\displaystyle b}$ are parameters.

This file was created with Python,NumPy and Matplotlib.

from __future__ import division
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import quad

plt.rcParams["axes.spines.top"] = False
plt.rcParams["axes.spines.right"] = False


def fun(alpha, beta):
    return np.sin(alpha)**2/np.sqrt(np.sin(alpha)**2 + beta)    
    
a = 1.
b = 0.8
beta = a**2/b**2
u = np.linspace(0, 9*np.pi, 500)
integral = np.array([quad(fun, 0, uval, args=(beta,))
					for uval in u])
x = integral[:, 0]
x = a*(1 - np.cos(u) + x)
y = a*(np.sin(u) + np.sqrt(np.sin(u)**2 + beta))
plt.figure(figsize=(5, 3))
plt.plot(x, y, lw=2)
plt.ylim([0, 3.0])
plt.savefig("Nodary.svg", transparent=True)
plt.show()

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

https://creativecommons.org/licenses/by/4.0CC BY 4.0 Creative Commons Attribution 4.0 truetrue