Previous investigations of the neural code for complex object shape have focused on two-dimensional pattern representation. This may be the primary mode for object vision given its simplicity and ...

The area of the rectangle is 8 cm 2. Two triangles make the rectangle. The area of one triangle is half the area of the rectangle. \(8 \div 2 = 4~\text{cm}^2\) The area of a triangle can also be ...

Two-dimensional (2D) shapes are completely flat. They cannot be picked up. 2D shapes can be found printed in a book or you can draw them on a piece of paper. 2D shapes have sides and corners (also ...

In an online lecture, a professor mentioned that Einstein could draw or imagine a 4-dimensional figure. How can one possibly do that? originally appeared on Quora: the knowledge sharing network where ...

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another. If you have two flat paper shapes and a pair of scissors, can you cut ...

Mathematicians, freed in their imaginations from physical constraints, can conjure up descriptions of objects in many more dimensions than that. Points in a plane can be described with pairs of ...

It can be tempting to assume that your intuitions about three-dimensional space carry over to higher-dimensional realms. After all, adding another dimension simply creates a new direction to move ...

These are not the kinds of objects that concern Scott Sheffield. Sheffield, a professor of mathematics at the Massachusetts Institute of Technology, studies shapes that are constructed by random ...