Things to make and do

65 entries

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• Braids in trivial braid diagrams
  • Published in 2003
  • Added on 2026-04-10
• A Note on Knots
  • Published in 1924
  • Added on 2026-03-02
• What Type of Apollonian Circle Packing Will Appear
  • Published in 2021
  • Added on 2026-02-26
• Incomplete Open Platonic Solids
  • Published in 2026
  • Added on 2026-02-26
• Polyform tiling
  • Published in 2012
  • Added on 2025-11-22
• Path planning for the Platonic solids on prescribed grids by edge-rolling
  • Published in 2021
  • Added on 2025-11-11
• Escher Tile Deformation via Closed-Form Solution
  • Published in 2025
  • Added on 2025-08-20
• Printable Puzzle Project
  • Published in 2019
  • Added on 2025-06-24
• The Paradox of Anti-Inductive Dice
  • Published in 2025
  • Added on 2025-05-23
• Squaring the Plane
  • Published in 2020
  • Added on 2025-01-07
• Hamiltonian Cycles on Ammann-Beenker Tilings
  • Published in 2024
  • Added on 2024-12-02
• (Non)existence of Pleated Folds: How Paper Folds Between Creases
  • Published in 2009
  • Added on 2024-12-02
• Ropes, fractions, and moduli spaces
  • Published in 2023
  • Added on 2024-09-30
• Tumbling Downhill along a Given Curve
  • Published in 2024
  • Added on 2024-07-24
• The Cardboard Computer
  • Published in 2024
  • Added on 2024-04-10
• Mathematical proofs with cardboard and paper
  • Published in 2023
  • Added on 2023-08-24
• Mathematical Marbling
  • Published in 2003
  • Added on 2022-07-12
• Pop-Up Geometry
  • Published in 2022
  • Added on 2022-02-16
• Fibbinary Zippers in a Monoid of Toroidal Hamiltonian Cycles that Generate Hilbert-Style Square-Filling Curves
  • Published in 2022
  • Added on 2021-12-08
• Bell-ringing methods as polyhedra
  • Published in 2015
  • Added on 2021-11-20
• Perimeter-minimizing pentagonal tilings
  • Published in 2014
  • Added on 2021-05-04
• The Amazing $3^n$ Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang]
  • Published in 2012
  • Added on 2021-03-15
• Programming the Hilbert curve
  • Published in 2004
  • Added on 2021-02-12
• Braids which can be plaited with their threads tied together at each end
  • Published in 1962
  • Added on 2021-02-12
• Envelopes are solving machines for quadratics and cubics and certain polynomials of arbitrary degree
  • Published in 2020
  • Added on 2021-01-06
• "Match-Stick" Geometry
  • Published in 1939
  • Added on 2020-12-20
• Paperfolding morphisms, planefilling curves, and fractal tiles
  • Published in 2010
  • Added on 2020-09-21
• Plane-filling curves on all uniform grids
  • Published in 2016
  • Added on 2020-09-21
• Computing Linkages
  • Published in 2010
  • Added on 2020-04-06
• Brainfilling Curves - a Fractal Bestiary
  • Published in 2012
  • Added on 2019-05-09
• Mathematics applied to dressmaking
  • Published in 1994
  • Added on 2018-11-29
• Duotone Truchet-like tilings
  • Published in 2009
  • Added on 2018-11-13
• Noncrossing partitions under rotation and reflection
  • Published in 2005
  • Added on 2018-10-27
• Enumeration of m-ary cacti
  • Published in 1998
  • Added on 2018-10-23
• On Some Regular Toroids
  • Published in 2001
  • Added on 2018-07-26
• Proof without Words: Fair Allocation of a Pizza
  • Published in 1994
  • Added on 2018-06-26
• A description of the outer automorphism of \(S_6\), and the invariants of six points in projective space
  • Published in 2008
  • Added on 2018-05-14
• Mechanical Computing Systems Using Only Links and Rotary Joints
  • Published in 2018
  • Added on 2018-01-30
• Folding Polyominoes into (Poly)Cubes
  • Published in 2017
  • Added on 2018-01-03
• Mechanisms by Tchebyshev
  • Published in 2009
  • Added on 2017-12-04
• A compilation of LEGO Technic parts to support learning experiments on linkages
  • Published in 2017
  • Added on 2017-12-04
• Maximum genus of the generalized Jenga game
  • Published in 2017
  • Added on 2017-08-07
• Overcurvature describes the buckling and folding of rings from curved origami to foldable tents
  • Published in 2012
  • Added on 2017-07-20
• Steinhaus Longimeter
  • Published in 2017
  • Added on 2017-07-02
• Ununfoldable Polyhedra with Convex Faces
  • Published in 2003
  • Added on 2017-06-26
• PVC Polyhedra
  • Published in 2017
  • Added on 2017-05-02
• Ovals and Egg Curves
  • Published in 2000
  • Added on 2017-04-03
• PAPAC-00, a Do-It-Yourself Paper Computer
  • Published in 1958
  • Added on 2017-03-21
• Rules for Folding Polyminoes from One Level to Two Levels
  • Published in 2017
  • Added on 2017-01-16
• Balloon Polyhedra
  • Published in 2013
  • Added on 2016-12-21
• Cryptographic Protocols with Everyday Objects
  • Published in 2011
  • Added on 2016-11-17
• Geometric Mechanics of Curved Crease Origami
  • Published in 2012
  • Added on 2016-10-14
• An Irrationality Measure for Regular Paperfolding Numbers
  • Published in 2012
  • Added on 2016-07-11
• Photoelectric Number Sieve Machine ("Gear Machine")
  • Published in 1932
  • Added on 2016-06-13
• On dice and coins: Models of computation for random generation
  • Published in 1993
  • Added on 2015-01-26
• A Mathematical Coloring Book
  • Published in 2009
  • Added on 2014-04-24
• Circular orbits on a warped spandex fabric
  • Published in 2013
  • Added on 2014-01-07
• A Do-It-Yourself Paper Digital Computer, 1959.
  • Published in 2010
  • Added on 2013-05-05
• Conway's Rational Tangles
  • Published in 2012
  • Added on 2013-02-06
• Papy's Minicomputer
  • Published in 1970
  • Added on 2012-10-31
• Train Sets
  • Published in 1994
  • Added on 2012-06-25
• Orange Peels and Fresnel Integrals
  • Published in 2012
  • Added on 2012-02-15
• Three-dimensional finite point groups and the symmetry of beaded beads
  • Published in 2007
  • Added on 2012-01-04
• Origami Burrs and Woven Polyhedra
  • Published in 2000
  • Added on 2011-12-14
• Laying train tracks
  • Published in 2011
  • Added on 2011-12-03