Math: I make up problems, often involving (discrete) sequences.* (Being interested in the problem helps.)
Reading.
*Without paper: Geometry:
a) What is the greatest distance in a cube? And what is it’s measure? In a tesseract (4-cube)? In the n-th hypercube?
b) What is the area of an equilateral triangle as a function of the length of one of its sides? The distance between the center and the corners? The distance between the center and the center of one of the sides?
With paper:
More general version of b): Consider the sequence of (regular**a) shapes with the least number of points for it’s number of dimensions. What is the the hyper volume of the n-th shape as a function of the distance between the center and a corner (it’s the same for all corners**b)?
**While I assert a → b, I haven’t proved this from the definition of regular polytopes.
Math: I make up problems, often involving (discrete) sequences.* (Being interested in the problem helps.)
Reading.
*Without paper: Geometry:
a) What is the greatest distance in a cube? And what is it’s measure? In a tesseract (4-cube)? In the n-th hypercube?
b) What is the area of an equilateral triangle as a function of the length of one of its sides? The distance between the center and the corners? The distance between the center and the center of one of the sides?
With paper:
More general version of b): Consider the sequence of (regular**a) shapes with the least number of points for it’s number of dimensions. What is the the hyper volume of the n-th shape as a function of the distance between the center and a corner (it’s the same for all corners**b)?
**While I assert a → b, I haven’t proved this from the definition of regular polytopes.