Carnival of Mathematics #236

Welcome to the 236th Carnival of Mathematics! 236 is the number of total partitions of 5. I drew up a graphic of the 26 total partitions of 4:

The total partition sequence is A000311 in the OEIS. It also describes the number of possible phylogenetic trees of n species in evolutionary biology.

The 2025th Carnival of mathematics is still quite a way off, so I hope its host won’t mind me stealing their thunder. At the turn of the year there was a fair amount of chat about 2025 being the sum of the cubes of 1 through 9, and related facts. The Mathematical Visual Proofs Youtube channel posted a video with a nice visual demonstration.

Submissions:

Colin Beveridge blogged about the scoring system at the 1995 World Figure Skating Championships, where the final skater posted a performance that left her in fourth place, but caused the places of the second and third place skaters to switch.

The Renaissance Mathematicus wrote a lengthy and rather critical review of The Secret Lives of Numbers: A Global History of Mathematics & Its Unsung Trailblazers, by Kate Kitagawa and Timothy Revell.

The Mathateca +Resource blog posted a much shorter review of Much Ado About Numbers by Robert Eastaway., along with links to related material about Elizabethan mathematics.

Brian Clegg posted the introduction to his book, A Brief History of Infinity, as the start of a (likely finite) series of posts on the topic of infinity.

Kit Yates posted about strategy in the game played on the UK reality show, Traitors. This game is appears to be the same one I know as Werewolf or Mafia, but played for high stakes reality game show prizes.

Kyle Hovey wrote a Tour of Haskell. Functional programming languages like Haskell have powerful type systems and syntax for manipulating functions that appeal to mathematical minds.

Zach M. Davis wrote about competing in the Putnam exam as a non-traditional college student at a college (San Francisco State University) without a history of participation.

Karen Campe wrote a pair of posts on using dynamic geometry software to aid students’ understanding. The first covers invariants, properties that do not change when you manipulate a figure. The second is on the difference between drawing a figure and constructing one.

Victor Poughon explored the problem of how to place a number of points on a disk as uniformly as possible. The post contains a nice mixture of mathematical reasoning, Python programming, and visual results.

John D. Cook posted about notation that makes Newton’s interpolation formula look like a Taylor series. I needed a refresher on Newton’s interpolation formula to appreciate it; I found this video by Will Wood to be helpful.

Bonus Carnival of Polyforms

Since I am a recreational mathematician who does a lot with polyominoes and other polyforms, (and because nobody is stopping me) I’m going to use this space to share some recent related material.

Numberphile recently released a couple of videos with Sophie Maclean on polyominoes. The first is an introduction to polyominoes, and what we know about how their numbers grow as a function of their size. The second is on polyomino achievement games, i.e., playing tic-tac-toe, where a given polyomino is the goal.

Lewis Patterson made a post on polycube puzzles where pieces fit into a 3×3×3 cube. The most famous of these is the Soma puzzle, but there are others!

Alexandre Muñiz [hmmm…] wrote a blog post about moves between polyform tilings.

The Puzzle Fun Facebook group remains the most active forum for polyform tiling problems. There have been some remarkable hexahex constructions recently from Roel Huisman (here) and Patrick Hamlyn (here).

Speaking of polyhexes, George Sicherman found some Pentahex Pair Tri-oddities.

And that’s a wrap! More info on the Carnival, and links to other instances of it, is available at the Aperiodical, the Carnival’s metahost.