Posted on September 17, 2026 in Society • Tagged with Mathematics, AI, Millennium-Prize-Problem • 6 min read
In November 2025, AI utterly changed software engineering. Now AI is writing better and more beautiful code than any human ever could, at dramatic speed. Why was there no letter by 25 Turing Award winners that AI "NEEDS TO STOP WRITING CODE" similar as Fields medallist wrote a letter when it became clear that AI is better at math than them?
Posted on October 06, 2013 in Learning • Tagged with Font, Captcha, Programming, Mathematics, Learning, Bézier • 13 min read
Last major Update: 21.10.2013
Github repo that contains the presented code in this post.
In this article I will present you a very simple and in no sense optimized algorithm written in Python 3 that plots quadratic and cubic Bézier curves. I'll implement several variants of Bézier rasterization algorithms. Let's call the first version the direct approach, since it computes the corresponding x and y coordinates directly by evaluation of the equation that describes such Bézier curvatures.
The other possibility is De Casteljau's algorithm, a recursive implementation. The general principle is illustrated here. But the summarize the idea very briefly: In order to compute the points of the Bézier curve, you subdivide the lines of the outer hull that are given from the n+1 control points [Where n denotes the dimension of the Bézier curve) at a ratio t (t goes from 0 to 1 in a loop). If you connect the interpolation points, you'll obtain n-1 connected lines. Then you apply the exactly same principle to these newly obtained lines as before (recursive step), until you finally get one line remaining. Consider again the point at the ratio t on this single line left and …