This page is a sub-page of our page on Expandable Learning Objects.
The sub-pages of this page are:
• Tesseracts for Flatlanders
• Einstein for Flatlanders
• Einstein for Linelanders
• The Linear War between the planets Vectoria and Vectoria’
• Shift of Basis for Stories
• Category Theory
• Functor Categories
• Naturally Related Functors and Processes
• Adjoint Functors
• Institution Theory
• The Human Category
• Business Algebra
• Clifford Algebra
• Geometric Algebra
• Linear Algebra
• Matrix Algebra
• Knowledge Algebra
• Discourse Algebra
• Social Algebra
• Socially Responsible Algebra
• Norm-Critical Innovation Algebra
• Some basic algebraic concepts
Other related sources of information:
• Flatland – the movie 2008, based on the novel Flatland by Edwin A. Abbott from 1884.
• Flatland – the limit of our consciousness
• A Wrinkle In Time, 2018 Disney film based on the novel by Madeleine L’Engle from 1962.
• How mathematicians are storytellers and numbers are the characters
Marcus du Satoy in The Guardian, 23 January 2015
Eleven stories designed to raise interest in mathematics
1. The story of the people who thought the world was understandable. From Thales and Pythagoras to Demokritos and Aristarkos.
2. The story of the people that wanted to escape the realm of the senses. From Plato via Augustinus and Aquino to the “scholastic age.”
3. The mathematics of the eye: The development of true perspective. From Pappus via della Franchesca and da Vinci to Desargues, Pascal, Poncelét, Plücker, Grassmann and Klein.
4. Einstein for Flatlanders: Two-dimensional relativity theory. The story about the flatlanders that lived on a sphere and the flatlanders that lived on a torus (“dough-nut”).
5. The story of the people that disregarded almost everything. The evolution of abstract thinking: From induction and abduction to abstraction and deduction. “The power of thinking is knowing what not to think about.”
6. On the difficulties of overcoming psychological complexes. The story about the development of the concept of number: From “positive” or “natural” to “negative”, from “rational” to “irrational”, from “real” to “imaginary” and “complex”.
7. What is there between the atoms? Does the world consist of particles or waves – or maybe something else? The historical debate from Thales versus Pythagoras via Newton versus Huygens to Einstein versus Bohr and Heisenberg and the break-up of the particle concept through the emergence of string theory and superstring theory.
8. The mysterious law about the degradation of work: The principles of energy and entropy. The development of the energy concept from Leibniz via Count Rumford and Carnot to Mayer, Joule and Boltzmann.
9. The story of the long-lived demon that was unable to forget. Maxwell’s demon and the deep connections between information theory and thermodynamics.
10. The evolution of geometric arithmetic.
11. Linear Algebra: The story of the linear war between the planets Vectoria and Vectoria’.