Curiosa mathematica, Part 1 : A new theory of parallels

In this surprisingly lively mathematics treatise, the author challenges the ancient foundations of Euclidean geometry by proposing a fresh axiom about inscribed shapes. Using the simple construction of an equilateral tetragon within a circle, he demonstrates how the familiar parallel postulate can be approached without invoking Euclid’s notorious twelfth axiom. The book balances rigorous proof with witty asides, making abstract reasoning feel almost conversational.

Readers are guided through two distinct sections: the first presents propositions that require no extra assumptions, while the second builds on the new axiom to tackle classic theorems about angles and triangles. Along the way, the author engages in a playful “dialogue with Nature,” defending his hypotheses with both logic and humor. The work invites anyone with a curiosity for geometry to glimpse how a single change in foundational thinking can open a whole new landscape of mathematical possibilities.