A point is a figure of no dimension.
A line is an infinite set of points in one dimension.
A polygon is a shape of two dimensions.
A cube is a shape with six sides in three dimensions.
Consider a four dimensional cube. What would it look like?
Given a set of 8 squares on a flat surface which can be arranged such that at least one of the sides of the squares is touching at least one side on another square what three dimensional shapes can be arranged?
What three dimensional shapes cannot be arranged? For the shapes that cannot be arranged explain why they cannot be developed from the set of eight squares.
Elementary calculus:
What is the sum of 1/3 + 1/6 + 1/9 + 1/12 ... 1/n as n approaches infinity. Is it divergent or convergent?
Can you apply this to further infinite series? Is there an algebraic method for calculating this?
Today I am going to spend some time working on some tiling problems, some problems in infinite series and some other items I am curious about. It will be a good day I hope.
If you are interested read this: http://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola
Then go read the work of Archimedes and the full QotP.
A line is an infinite set of points in one dimension.
A polygon is a shape of two dimensions.
A cube is a shape with six sides in three dimensions.
Consider a four dimensional cube. What would it look like?
Given a set of 8 squares on a flat surface which can be arranged such that at least one of the sides of the squares is touching at least one side on another square what three dimensional shapes can be arranged?
What three dimensional shapes cannot be arranged? For the shapes that cannot be arranged explain why they cannot be developed from the set of eight squares.
Elementary calculus:
What is the sum of 1/3 + 1/6 + 1/9 + 1/12 ... 1/n as n approaches infinity. Is it divergent or convergent?
Can you apply this to further infinite series? Is there an algebraic method for calculating this?
Today I am going to spend some time working on some tiling problems, some problems in infinite series and some other items I am curious about. It will be a good day I hope.
If you are interested read this: http://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola
Then go read the work of Archimedes and the full QotP.