Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes ...

Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars ...

Transformations change the size or position of shapes. In the exam you may be asked to draw and/or describe transformations. In Module 8 (M8), there may be questions on any of the transformations work ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...