PM2Ring

(0, 1) : 50
(1, 0) : 50
(0, 2) : 258
(1, 1) : 600
(2, 0) : 258
(0, 3) : 186
(1, 2) : 1086
(2, 1) : 1086
(3, 0) : 186
(0, 4) : 5

PM2Ring

PM2Ring

#!/usr/bin/env python3

''' Create a closed track from cubic Bezier curves, and animate a circle
    following the track at constant speed.

    https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B%C3%A9zier_curves
    
    https://gist.github.com/PM2Ring/d6a19f5062b39467ac669a4fb4715779
    
    Press the Add button to add black control dots to the Canvas. The first

PM2Ring

#! /usr/bin/env python3

''' Demonstrate the PIL .fromarray bitmap bug

    PIL's Image.fromarray function has a bug with mode '1' images

    See
    https://stackoverflow.com/questions/2761645/error-converting-pil-bw-images-to-numpy-arrays

    Written by PM 2Ring 2017.06.26

PM2Ring

""" Julian day number to date conversion
    Proleptic Gregorian and Julian, with Astronomical years
    i.e., 1 AD = year 1, 1 BC = year 0, 2 BC = year -1, etc

    Derived from RG Tantzen (1963), ACM.
    Algorithm 199: conversions between calendar date and Julian day number.

    https://en.wikipedia.org/wiki/Julian_day
    Julian day number 0 assigned to the day starting at noon on
    January 1, 4713 BC, proleptic Julian calendar

PM2Ring

""" Maxwell–Boltzmann distribution
    See https://en.m.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
    Written by PM 2Ring 2021.06.20
"""
# Gas constant g⋅m^2⋅s^−2⋅K^−1⋅mol^−1
R = 8314.46261815324

@interact
def _(T=('temp (°C)', 20), mass=('mass (g/mol)', 29),
  auto_update=False):

PM2Ring

""" Lorenz attractor 

    From https://en.wikipedia.org/wiki/Lorenz_system
    Modified for Sagemath by PM 2Ring 2023.01.04
"""

import numpy as np
from scipy.integrate import odeint

# Build Bezier curves

PM2Ring

""" Borwein + Borwein quadratic pi
    Algorithm 2.1 from "Pi and the AGM" (Wiley, 1987)

    Written by PM 2Ring 2023.1.2
"""
from math import floor, log, pi
from decimal import Decimal as D, getcontext

def borwein_pi(loops):
    x = D(2).sqrt()

PM2Ring

Standard Solar Model (BP2004)
https://www.sns.ias.edu/~jnb/SNdata/Export/BP2004/bp2004stdmodel.dat
astro-ph/0402114

Columns in the Standard Model table (below) represent:

1)  Mass fraction in units of the solar mass
2)  Radius of the zone in units of one solar radius
3)  Temperature in units of deg (K)
4)  Density in units of g/cm^3

PM2Ring

#! /usr/bin/env python3

''' Generalization of the 'Fitch' Cheney card trick

    Written by PM 2Ring 2003.02.13
    Converted to Python 2018.06.27
'''

import sys
import readline