Archiv der Kategorie Euler

Python in EMT – Cross Sum of Cubes

When is the cross sum (sum of the digits) of the cube of a number equal to the number? It is obviously true for n=0 and n=1. You might be able to find n=8 with the cube 512. Then, how … Weiterlesen

30. März 2017 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Recursion Formulas

I do not know if I ever wrote about this. But it is a well known theory, anyways. To find a formula for the Fibonacci numbers $$F_{n+1} = F_n + F_{n-1}, \quad F_0 = 0, \quad F_1 = 1$$ you … Weiterlesen

22. März 2017 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Image Processing and Data Evaluation in EMT

There is an example for Euler Math Toolbox (EMT) where I tried to fit curves to a real chain. I then fitted a parabola and a catenary to the points and explained a bit about the catenary. The points where … Weiterlesen

04. August 2016 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

The Bayesian and the Frequentist – III

For another story, I read the following problem on a Google+ site yesterday: You have three cards in your pocket, one with two red sides, one with two blue sides and one with a red and a blue side. You … Weiterlesen

24. Juli 2016 von mga010
Kategorien: English, Euler, PISA | Schreibe einen Kommentar

The Bayesian and the Frequentist – II

This is not immediately related to Bayesian statistics. But it is a good argument for the frequentistic approach. I met the problem in  a Youtube video, but the core of this problem is well known. The solutions are not always … Weiterlesen

20. Juli 2016 von mga010
Kategorien: Euler, Uncategorized | Schreibe einen Kommentar

Units in Euler Math Toolbox

Units have long been an integral part of EMT. I want to show you a few examples. First, let us talk about the non-metric system the US is still using. Quote: „Nobody understands the metric system! We use teaspoons!“. >1inch … Weiterlesen

08. April 2016 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Solving Partition Problems with Linear Programming

Yesterday I promised to show how to solve partition problems with integer linear programming. Let us take the problem of yesterday: We want to split the numbers from 1 to 30 in 10 triplets (x,y,z) such that x+y+z=0 modulo 31. … Weiterlesen

30. März 2016 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Modulo Arithmetic with Euler Math Toolbox

Recently, I came across the problem to compute expressions in the modulo arithmetic with integer numbers. Here is an example: We like to compute expressions modulo 31. Since 31 is prime the numbers 0 to 30 with addition and multiplication … Weiterlesen

29. März 2016 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Euler Math Toolbox and Matlab

Recently, this site got more traffic than usual. So I thought I welcome all of you in the new year (which is already three weeks old now). And I provide some new content for you to read. For me, the … Weiterlesen

25. Januar 2016 von mga010
Kategorien: English, Euler | 2 Kommentare

Pure Symbolic Functions in Maxima and EMT

I like to demonstrate a few tricks with Maxima and EMT. Assume you want to generate the Vandermonde matrix, and check the identity \(\det \begin{pmatrix} 1 & x_0 & \ldots & x_0^n \\ \vdots & \vdots &  & \vdots \\ … Weiterlesen

12. Dezember 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

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