Researchers have solved a long-standing problem in topology by helping classify four-dimensional shapes (4-manifolds) that ...

A mathematical problem solved by Susanna Heikkilä relates to the classification of quasiregularly elliptic 4-manifolds, ...

They discern one another's shape both by touching and by seeing ... the square conceives the possibility of a fourth dimension. He even goes so far as to suggest that there may be no limit to ...

This is difficult to visualize, as we can only perceive the world around us as a three-dimensional space, and even more challenging to measure. An example of a four-dimensional object is the ...

Loci can be used to accurately construct lines and shapes. Bearings are three figure angles measured clockwise from North. 2-dimensional shapes - Edexcel 2-dimensional shapes are flat. The ...