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).
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).
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: https://www.shapeways.com/shops/Feingold_Math_Art But there are a huge number of other artists whose work can also be found in other shops there.
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."
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?)
I have a Rattleback at my desk. Fun to fiddle with while thinking.
The Rubik cube. ${}{}{}{}{}{}{}$
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.
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.
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.
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.
The Oloid is fun to touch, to watch and understand.
Maybe a Tippe Top.
Love zometool [1]
[1]: http://www.zometool.com/ for geometry, platonic and archimedean solids, among others/
I think there are 2 different toy devices that mimic a Gray code. One can be seen at http://mypuzzlecollection.blogspot.com/2011/12/brain.html. The other is named "Spin Out".
Sudoku and all other logic trainers would also fit.
Check Montessori mathematical materials like the binomial cube just google it
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.