Mathematicians Cut Apart Shapes to Find Pieces of Equations

Scissor congruence

Two flat paper shapes are considered "scissors congruent" if you can cut up one shape and rearrange it as the other.  But is there a way to determine this relationship if you don't have scissors?  Are there characteristics you could measure ahead of time that would determine this, and would they apply to both two and higher dimensional shapes?  These questions have been pondered by mathematicians for over a century.  

This fall Jonathan Campbell of Duke University and Inna Zakharevich of Cornell University presented a paper at the University of Chicago that took a significant step toward proving scissors congruence for shapes of any dimension.  They also may have given mathematicians a new way of thinking about algebraic equations.

Read the article in Quanta magazine:  https://www.quantamagazine.org/mathematicians-cut-apart-shapes-to-find-pieces-of-equations-20191031/

Scissors Congruence

Lucy Reading-Ikkanda/Quanta Magazine