Koch’s Snowflake in Python

# Draw a Koch snowflake
from turtle import *

def koch(a, order):
    if order > 0:
        for t in [60, -120, 60, 0]:
            forward(a/3)
            left(t)
    else:
        forward(a)

# Test
koch(100, 0)
pensize(3)
koch(100, 1)

Now, we make a small change to the function koch:

    for t in [60, -120, 60, 0]:
            koch(a/3, order-1)
            left(t)

Completed code:

# Choose colours and size
color("sky blue", "white")
bgcolor("black")
size = 400
order = 0

# Ensure snowflake is centred
penup()
backward(size/1.732)
left(30)
pendown()

# Make it fast
tracer(100)
hideturtle()

begin_fill()

# Three Koch curves
for i in range(3):
    koch(size, order)
    right(120)

end_fill()

# Make the last parts appear
update()

Source.

A Biography of Émile Lemoine

In the link below, a brief biography of mathematician Emile Lemoine, responsible for the Lemoine point of a triangle and Lemoine’s Conjecture, sometimes attributed to the later work of Hyman Levy.  Lemoine’s Conjecture is a stronger form of the Goldbach Conjecture.

Biography: Emile-Michel-Hyacinthe Lemoine
Author(s): David Eugene Smith
Source: The American Mathematical Monthly, Vol. 3, No. 2 (Feb., 1896), pp. 29-33
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/2968278
Accessed: 25-01-2018 02:40 UTC

Full Biography