Anybody know of "serious" mathematical ornaments or toys like the Gömböc, etc?
Already have a rubix and abacus (that's more of a tool though).
$\endgroup$ 318 Answers
$\begingroup$For when the Möbius strip is too pedestrian, the good people at Acme Co. claim their Klein bottles are the "finest closed, non-orientable, boundary-free manifolds sold anywhere in our three spatial dimensions."
$\endgroup$ 1 $\begingroup$On Shapeways, you can find a variety of mathematical ornaments.
My favorites are the differential geometric surfaces designed by Bachman. I also like Bathsheba's designs as well.
(Sorry the image is so large. Is there a way to reduce the size?)
$\endgroup$ $\begingroup$I have a Rattleback at my desk. Fun to fiddle with while thinking.
$\endgroup$ $\begingroup$The Rubik cube. ${}{}{}{}{}{}{}$
$\endgroup$ 1 $\begingroup$Spirograph from Hasbro. You can make lots of famous mathematical curves with its pieces: epicycloids, hypocycloids, etc. MathWorld has an article on some of these curves.
$\endgroup$ 1 $\begingroup$Zometool is a construction kit which has 2-, 3-, and 5-fold symmetry, which is great for building (3D projections of) the 120-cell, or just for playing around.
$\endgroup$ 1 $\begingroup$Wikipedia has a section on mechanical puzzle.
As for myself, my fascination with algebraic topology began with metal link puzzles or hanayama.
Of course, Tower of Hanoi is a classic.
Of interest may be the reference: Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys by David Joyner. Book description in Amazon.
$\endgroup$ $\begingroup$While it may be a 'children's toy', the Switch Pitch works remarkably well as an object of mathematical sculpture; it's fundamentally based on the fact that the vertices of a regular cube are also the vertices of two (interlocked) regular tetrahedra (if your cube is $\{0,1\}^3$, take the vertices with $i+j+k$ respectively odd or even). It helps that people can't help but fiddle with it; it's been a perfect hand-fidgetting toy for me.
$\endgroup$ $\begingroup$The Oloid is fun to touch, to watch and understand.
$\endgroup$ $\begingroup$Maybe a Tippe Top.
$\endgroup$ $\begingroup$Love zometool [1]
[1]: for geometry, platonic and archimedean solids, among others/
$\endgroup$ $\begingroup$ $\endgroup$ $\begingroup$Goal: Remove the big ring
$\endgroup$ $\begingroup$I think there are 2 different toy devices that mimic a Gray code. One can be seen at . The other is named "Spin Out".
$\endgroup$ 1 $\begingroup$Check Montessori mathematical materials like the binomial cube just google it
$\endgroup$ $\begingroup$Sudoku and all other logic trainers would also fit.
$\endgroup$ $\begingroup$Origami to fold shapes to find surface area of 3 dimensional shapes. Wooden blocks. The Game of 24. Math Jeopardy. Bucky balls. Sudoku. Computer games with rotations and other types of transformations.
$\endgroup$ $\begingroup$In a blatant reference to my own creative work, I submit for your consideration the mathematical artwork presented on my Shapeways Shop at this address: But there are a huge number of other artists whose work can also be found in other shops there.
$\endgroup$
