2016-07-30, post № 135
programming, Pygame, Python, #clock, #complex number, #hour, #minute, #plane, #time
Interpreting the hour hand on a clock as a two-dimensional object on a plane, the hand’s tip can be seen as a complex number.
This clock converts the hour hand’s position into a complex number, sets the number’s length to the current minutes and displays it in the form .
The angle 𝜑 is determined by the hours passed () but has to be slightly modified because a complex number starts at the horizontal axis and turns anti-clockwise whilst an hour hand starts at the vertical axis and turns — as the name implies — clockwise. Thus, .
The complex number’s length is simply determined by the minutes passed. Because the length must not be equal to 𝟢, I simply add 𝟣: .
Lastly, to convert a complex number of the form into the form , I use the formula .
2016-07-23, post № 134
programming, Python, #calculation, #date, #day, #month, #time, #year
Determining the weekday based on a date composed of day, month and year.
The program counts up all the days from the 1st of January 1 to the given date, divides it by 𝟩, looks at the remainder and returns the weekday.
2016-07-16, post № 133
programming, Python, Wolfram Language, #equation, #number, #number theory, #numbers, #OEIS, #square, #triangle, #triangles
In a recent video, Matt Parker showed a triangular number that also is a square number, 𝟨, and asked if there were more.
A triangular number has the form — shown by Euler — and a square number has the form .
Triangular squares are those numbers for which with .
Examples are (sequence A001109 in OEIS).
To check if triangular numbers are square numbers is easy (code listed below), but a mathematical function would be nicer.
The first thing I tried was to define the triangular number’s square root as a whole number, . This function does not return the square numbers that are triangular but the triangular numbers that are square.
The resulting sequence is (sequence A001108 in OEIS).
Jonathan Frech's blog; built 2021/04/16 21:21:49 CEST