Archives - 2019

Gallery Bakeoff Article from MensaNZ

Open Mic Maths

Session A (Saturday)

Mark Houghton: Drunken Sequences

Mark gave a talk on undirected graphs, and figuring out the expected travel length. How many steps will it take, starting at A and terminating when reaching D, for various four-node graphs, if the travel direction from any node is picked with equal probability?

Nic Petty: Divisibility by 7

Nic demonstrated a trick to determine if a number is divisible by 7: simply take the last digit and multiply it by 5, then add this to the remaining digits. Do this recursively until you can tell the number is or is not divisible by 7.

Josie Smith: Hilbert’s Hotel

Josie introduced us to Hilbert’s Hotel, where there’s an infinite number of rooms and they’re all occupied. Then, some more guests show up, and that’s no problem for Hilbert’s Hotel! With some clever shuffling, all guests get a room. Then an infinite coach of extra guests shows up, then a ferry carrying infinite coaches… followed by infinite more ferries… still no problem for Hilbert’s Hotel!

Chris Hext: Fibonacci numbers in Pascal’s Triangle?

Chris talked about the Pascal-Fibonacci problem, see demonstration for case n = 9 [pdf]. He challenges the reader to come up with a general proof of why it works for any n. The most elegant proof submitted before the next OMG will win a small prize. Submit your proofs to nzgathering@mathsjam.com.

James McGowan: World Puzzle Champs

James, the number one Puzzle Grand Prix solver in New Zealand, gave us an overview of what it’s like to enter the world puzzle championships, and showed us how to approach the logic puzzle “skyscrapers”.

Chris Wong: Sound and Harmony

Chris gave a talk about what harmony means from the perspective of music theory. Read his slides here: [pdf]

Tom Vavasour: 8 out of 10 sheep can’t count down

In the evening, Tom ran a game based on “8 out of 10 cats does Countdown” while discussing mathematical Countdown trivia. Tom's discussion was inspired by this analysis

Session B (Sunday)

Mark Houghton: Alice Checkers

Inspired by Alice Chess and with no immediate access to a chessboard, Timaru MathsJam organiser Mark tried an analogous version of checkers on two 5x5 board. “Alice checkers” was the result. Every move of a counter teleports it to the same position on the other board. The question is, is this a feasible game?

Kirk Alexander: NSA

Kirk gave us a talk/puzzle about a mysterious geometric shape on the cover of one of his father’s poetry books, NAMES [cover]. His talk was a tribute to his father Noel S. Alexander (NSA), who had recently passed away. Kirk has read the following passage in his talk:

The cover design represents the entire realm of human relationships as background to my family circle, with one square symbolising the four children of my parents and the other square standing for my own four children.

— Noel S. Alexander, NAMES

He also shared two puzzles with the audience:

  1. for the mystically inclined - what is the centre of the circle?
  2. for the mentally agile - prove that the area of the octagon is about 53% of the area of the circle.

Ross Atkins: Pi from Scratch

Ross asked how does a calculator figure out answers beyond the four basic functions. He demonstrated a simple algorithm to calculate square roots, then set a challenge: calculating pi to 8 decimal places in 8 minutes.

Rata Ingram: What is a Calculator?

Rata gave a talk on what qualifies as a calculator, from abacuses to programmable calculators, using some 15 varied examples from her nascent calculator museum. The “performing monkey” calculator was popular. Read the talk/slides here: [pdf with notes]

Huba: Fuzzy Logic

Huba gave an introduction to fuzzy logic. Using the analogy “you are walking into a forest where the trees start sparsely and get denser, at what point does it become a forest?” he talked about how it can be useful to have a truth value anywhere along the unit interval when evaluating set membership, instead of treating the question as a boolean one.

Andre MacLeod: Mathematical Poems

Andre showed us the mathematical limerick:

a dozen, a gross and a score
plus three times the square root of four,
divided by seven,
plus five times eleven,
equals nine squared and not a bit more.

And then proceeded to write his own mathematical limerick on stage.

Keynote Talk: 1, 3, 2, 6, ... what comes next?

Our keynote was open to the public as well as OMG attendees, and Dr Ross Atkins took the audience on a journey of discovery, exploring some of the patterns that emerge from a particular sequence beginning with 1,3,2,6. The talk covered a wide range of “completely unrelated” topics, including the Golden Ratio, Rayleigh's Theorem and Game Theory, and led to an extended Q&A (and ABABA) session.

Dr Ross Atkins completed his PhD in Mathematics at Oxford University, and is a trainer for the New Zealand Mathematical Olympiad Team. His interests include mathematics, puzzles and juggling.

Watch the keynote talk on YouTube: https://youtu.be/W27TwG8iB_s

Resources

Thanks To

Thanks to everyone that made the first OMG2019 happen, especially