## Sunday, September 21, 2014

### Pascal's triangles in HTML5

I did this animation in Flash long time ago, but I wanted to see it on my iPhone so I ported it to JavaScript using canvas and web audio.

Labels:
canvas,
javascript,
math

## Sunday, August 24, 2014

### Mathematical art

Once upon a time, I considered myself a decent painter. I remember getting second place in some magazine for some Christmas teenagers contest and spending a whole summer painting furiously at my home in the highlands. But, truth be said, I'm awful compared with the professional painters and artists I have found working as a game developer. Most of my art prodigies are forever lost now, maybe for good, but I remember painting something like this when I was entranced on my abstract expressionism period:

Labels:
canvas,
javascript,
math

## Sunday, January 5, 2014

### IMO 1979 Problem 3

I "solved" another International Mathematical Olympiads problem:

Inverse direction
The source code can be found here: http://github.com/ex/js

And the stand alone demo can be viewed here: http://ex.github.io/js/src/imo_1979_3/

There are two circles in the plane. Let a point A be one of the points of intersection of these circles. Two points begin moving simultaneously with constant speeds from the point A, each point along its own circle. The two points return to the point A at the same time. Prove that there is a point P in the plane such that at every moment of time the distance from the point P to the moving points are equal.The demo below draws all the lines that satisfy the condition while the points are moving, if there is such a point P then our lines must intersect in that point.

**r (R1/R2)**

**q [R1 - R2, R1 + R2]**

**Move**

And the stand alone demo can be viewed here: http://ex.github.io/js/src/imo_1979_3/

Labels:
code,
javascript,
math

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