Popular math writers Robert and Ellen Kaplan (*Out of the Labyrinth: Setting Mathematics Free*, 2007, etc.) examine the far-reaching, and at times exotic, applications of the familiar theorem.

With its origin traced back as far as ancient Babylon, the properties inherent in the Pythagorean Theorem (A *squared* + B *squared* = C *squared*) have had myriad implications both pedestrian and profound, from basic land-area assessment to architecture to physics. Thousands of people have worked out Pythagorean proofs, including President James Garfield while he was in the House of Representatives—further testament to both its alluring nature and astonishing versatility. (Interestingly, Pythagoras is not believed to have formulated the theorem named after him, which only adds to the mystique.) From a modern perspective, everything from differential calculus to astronomy utilizes the theorem’s principles, and it has even been proven to apply to figures in multiple dimensions, up to infinity, and to hint at the intriguing realm of irrational numbers. The authors, whose enthusiasm and wit make the material appealing even to readers who aren't mathematicians, write that such inspired deductions provide “the giddy sort of sensation that often leads people into mathematics: grasping something infinite via abstraction (as children love dinosaurs, because they are both very big and not quite real).” The book contains a healthy number of equations and proofs, some of which are intimidating, but the authors maintain an engaging plainspoken narrative peppered with references to, among many others, Shakespeare, Jefferson, Freud, Einstein and Descartes. It’s clear that this theorem continues to play an important role in math and science, that the human capacity for theoretical exploration remains unabated and that our “curiosity always seeks to justify the peculiar, and imagination to shape a deeper unity.” As such, this engaging history of the elegantly simple theorem provides readers with much more to ponder than just the mathematical.

May not be widely accessible, but for the right reader, an enthralling exploration of this ancient rule of ratios.