Laurent Lessard

Using* the most cursed #ALevelMaths Formula in #MathsToday

*absolutely not using but fun as a hook for Radians Sector lesson with Y12

Wow. it must feel terrible when someone takes something you made and uses it without permission or payment

This week's #Fiddler puzzle is a random walk: From (k), you hop to (k-1) with probability 1/k and hop to (k+1) otherwise. If you start at (2), what is the probability you eventually hop to (1)? @xaqwg.bsky.social

I wrote a short tutorial here:
laurentlessard.com/bookproofs/c...

This week's #Fiddler: Assign distinct prime numbers to the vertices of a dodecahedron so the sum of the vertices of each face sum to 2025. I modeled this as an integer linear program. Here is one possible solution. @xaqwg.bsky.social

My write-up: laurentlessard.com/bookproofs/2...

Print your pdf to pdf and then try again! Seriously!

More fun: if you assume the energy function is 1/r^k, then the regular lattice is optimal for k > 1.067 and the irregular arrangement is optimal for k < 1.066. 🤷‍♂️

Interestingly, if energy is instead measured as 1/dist², then the regular lattice becomes the optimal arrangement!

This week's #Fiddler: what is the minimum-energy way to pack 9 particles in a unit square, where energy is measured as the sum of 1/dist over all pairs of particles?

Turns out it's NOT a regular 3x3 lattice! @xaqwg.bsky.social

write-up:
laurentlessard.com/bookproofs/p...