We often want to reduce something that's inherently two-dimensional into something one-dimensional. We want to turn graph into a list. And we'd like to do this with some kind of faithfulness. We'd like things that are close together in 2D space to be close…

Counting the number of points on an elliptic curve using a crude algorithm, a better algorithm, and the best algorithm.

Memorable prime numbers with various numbers of digits. For example, if you need a five-digit prime, you could say 18181.

Plotting the points on an elliptic curve over a finite field can be very misleading.

Pi is the ratio of a circle's circumference to its diameter. You can generalize pi to pi_p by generalizing the notion of circle and the notion of circumference.

The Tiny Jubjub curve is an elliiptic curve designed to be similar to other Jubjub curves, but small enough for hand calculations.

Since the way we manipulate high-dimensional vectors is primarily matrix multiplication, it isn’t a stretch to say it is the bedrock of the modern AI revolution. The post A Bird’s-Eye View of Linear Algebra: Why Is Matrix Multiplication Like That? appeared…

Converting elliptic curves between Weierstrass, Montgomery, and twisted Edwards form. Using Baby Jubjub and Tiny Jubjub as examples.

A prime number that looks like a blackand-white image of an American flag when written in a block.

Python integers can be arbitrarily long, but there are limits on the size of string that you can convert to an integer. How to get around this limit.

A simple random process that produces the Twin Dragon fractal.

If you remember the words in a seed phrase out of order, try permutations in order of their permutation distance from what you remember.

An ingenious device for factoring integers from the days before computers. A set of around 300 stencils could factor 9-digit numbers.

Creating interesting images by connecting the partial sums of a series involving the exponential of complex numbers.

When does log x equal x with the decimal place moved? First we look at the problem for base 10, then for more general bases.

A general recipe for creating randomly-generated fractals that tile the plane.

Learn why autoregressive flows are the superior density estimation tool for high-dimensional data The post Cracking the Density Code: Why MAF Flows Where KDE Stalls appeared first on Towards Data Science. Generated by RSStT. The copyright belongs to the original…

Knuth defines the twindragon fractal to be the set of complex numbers that are "fractions" in base 1-i. Implemented in Python code.

Pick's theorem computes the area of a figure drawn on a grid by counting the number of grid points inside and on the perimeter, but the formula isn't obvious.