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The Math Less Traveled
mathlesstraveled.com · Personal blog · on HN since 2009
Joshua Bowman writes The Math Less Traveled, a blog of recreational math, visualizations, and number theory with Haskell code and diagrams.
What HN saysHN commenters link its factorization diagrams as a visualization they find brilliant and want to build on, and as a clear explanation of the algorithm.
23HN people shared it
10linked it in comments
19stories submitted
217story points
1 year agolast shared
2009people per year2026
Most-shared posts
- 1Factorization diagrams in Haskell4 people · 103 points · first shared 2012 · 19 comments on HN
- 2A new way to read and print double-sided paper (2016)2 people · 46 points · first shared 2016 · 26 comments on HN
- 3Random cyclic curves in the complex plane2 people · 3 points · first shared 2017 · discussion on HN
- 417×17 4-coloring with no monochromatic rectangles2 people · 2 points · first shared 2012 · discussion on HN
- 5More factorization diagrams2 people · first shared 2012
- 6Euclid's Orchard, the Euclidean algorithm, and Fibonacci numbers, with pictures1 people · 32 points · first shared 2017 · discussion on HN
- 7We can make primality machines that do not know anything about the factors of n1 people · 19 points · first shared 2018 · 5 comments on HN
- 8Fermat’s Little Theorem: proof by necklaces1 people · 3 points · first shared 2017 · discussion on HN
- 9Manufactoria: A computer science teaching game1 people · 2 points · first shared 2010 · discussion on HN
- 10The Math Less Traveled: Post Without Words #111 people · 1 points · first shared 2018 · discussion on HN
- 11Cosmic Call at the Universe of Discourse – The Math Less Traveled1 people · 1 points · first shared 2015 · discussion on HN
- 12Making the Fermat primality test deterministic1 people · 1 points · first shared 2019 · discussion on HN
- 13John Conway’s algorithms for counting stairs1 people · 1 points · first shared 2020 · discussion on HN
- 14Visualizing Pascal's triangle remainders1 people · 1 points · first shared 2012 · discussion on HN
- 15Did you know the number 86 was so interesting?1 people · 1 points · first shared 2012 · discussion on HN
What HN people wrote when they linked it
slackenerny · 2009-06-13
My favorite way, though, is just to make a grid of pairs of integers (numerator, denominator), and then count them by spiraling outward on the grid. This yields duplicates, but that's ok.
Calkin and Wilf cleverly avoid duplications by arranging reals not on a lattice but on a (Stern-Borcot) tree.
http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree
http://www.mathlesstraveled.com/?p=94
worldsayshi · 2025-05-21
This is brilliant!
Now i want (to build) a drag and drop toy where i can multiply or summarize numbers that are represented in this way. To see how factors move (like boids).
Is this visualization algorithm called something? The explanation link from a previous HN post seems to be broken: http://mathlesstraveled.com/2012/10/05/factorization-diagrams/
tuukkah · 2022-11-13
It tells about the factorizations if anything, as that's the input dimensions they are using. If you haven't seen factorization diagrams, it's worth checking them out first: https://mathlesstraveled.com/factorization/
But visualisations can always deceive you into seeing something that's not there, e.g. correlation vs causation.
dahart · 2017-10-04
That was awesome thanks for sharing. For the first minute I wasn't expecting much, but the reflections part was so cool! Plus, this connects directly to the cyclic curves in the complex plane, e.g., https://mathlesstraveled.com/2015/06/04/random-cyclic-curves-5/ The curves formed by the envelope of intersecting lines in the circular multiplication table are a slice of cyclic curve space. I animated this after reading the above blog post: https://youtu.be/myGXoLCnx-A You can see some of the curves in the lower left corner are the same ones from Mathologer.
chubot · 2015-12-22
Very interesting. Here is a nice explanation of the algorithm:
http://mathlesstraveled.com/2012/10/05/factorization-diagrams/
(from the "About" page)
gtani · 2013-01-06
cryogenics section, for potential resuscitation of
mathematical campaigns using future technology
automated provers like coq and isabelle, I think (I also think I'm not a crackpot but ...
http://arxiv.org/abs/1211.7012
http://mathlesstraveled.com/2012/11/11/a-computer-checked-proof-of-the…
Probably the haskell/agda camp'll want to defend their honor also
sold · 2012-11-15
jameskilton · 2012-02-12
For those of us who are confused what "monochromatic rectangles" actually means, this article shows it perfectly:
http://mathlesstraveled.com/2012/02/09/17x17-4-coloring-with-no-monoch…
imurray · 2011-08-16
http://mathlesstraveled.com/2011/06/04/the-collatz-conjecture-is-safe-…
(At the end of the comments you'll see that the author of the proof withdrew the claim.)