#farey sequence

[sqrt-73]

Interesting math fact of the day #59:

Let c/d be the smallest fraction greater than a/b with a denominator <= n. Then bc = ad + 1.

Ex:

n = 5, a/b = 1/3

c/d = 2/5

ad = 5, bc = 6

n = 1,000,000, a/b = 1/3

c/d = 333,333/999,998

ad = 999,998, bc = 999,999

[right-fold]

Ford gets Complex!

[latexpage]

    Not too complicated and just a different view of Ford’s circles and a way of morphing them along with a bit of animation.

http://gitcommit.co.uk/wp-content/uploads/2018/06/rotated-1.mp4

It’s a continuation of the previous post and there are two parts to it – the real bit and the imaginary part.

The Real Part

To start with we take fractions not between 0 and 1 but rather between…

View On WordPress

[right-fold]

Count the Fractions.

[latexpage] This is the first in a series of posts about sequences of fractions, circles, trees of fractions, binary search trees and ways of representing rational numbers as paths through these trees . The idea is to enjoy a bit of recreational mathematics and to use Haskell to express some of the notions in its own succinct  way.

One Lot Of Fractions

First we’ll look at all unique and simplified…

View On WordPress