About this book
Contents
Dossier 1: From Various Angles
The mention of polygons generally brings to mind the geometric figures of our tessellations, often regular. Their apparent simplicity might lead one to believe that their study is without difficulty, hence without interest. Yet, some operations remain complex.
Topics covered
What is a polygon? Albert Girard, the precursor of classifications Polygon taxonomy Some constructions Regular polygons Geometric irrationality The birth of a star Symmetry groups, a powerful tool Hiking in Polygonia
Dossier 2: From Classics to the Summit
Since Antiquity, people have been interested in calculating the area of a quadrilateral and simple polygons. These questions still give rise to developments. Another ancient problem, the construction of regular polygons with straightedge and compass.
Topics covered
Pick, an inspiring theorem Integer polygons Pythagoras Heron Heptadecagon: true or false Robbins' pentagons Napoleon, geometer of the world
Dossier 3: The Universe of Quadrilaterals
Quadrilaterals are generally presented and classified as subcategories of the parallelogram. This leads to thinking that any general quadrilateral would have no interest. What an error! Very beautiful properties are enjoyed in the most general cases.
Topics covered
Meeting quadrilaterals This is not a square Convex quadrilaterals Circumscriptible quadrilaterals Orthodiagonals Extending to complete
Dossier 4: A World with Multiple Sides
Polygons extend well beyond the strict framework of geometry, with practical or recreational applications. They are found, for example, in architecture or arithmetic. They are naturally the tesserae of many puzzles and subjects of a vast field of mathematical recreations.
Topics covered
When polygons form numbers Pentacles and pentagrams The quadrature of polygons Einstein hat! The single cut theorem The hidden riches of the multiplication table The Castel del Monte The Château de Maulnes The vertex polygon, a polygon at the summit! The Petrie polygon
Dossier 1: From Various Angles
The mention of polygons generally brings to mind the geometric figures of our tessellations, often regular. Their apparent simplicity might lead one to believe that their study is without difficulty, hence without interest. Yet, some operations remain complex.
Topics covered
What is a polygon? Albert Girard, the precursor of classifications Polygon taxonomy Some constructions Regular polygons Geometric irrationality The birth of a star Symmetry groups, a powerful tool Hiking in Polygonia
Dossier 2: From Classics to the Summit
Since Antiquity, people have been interested in calculating the area of a quadrilateral and simple polygons. These questions still give rise to developments. Another ancient problem, the construction of regular polygons with straightedge and compass.
Topics covered
Pick, an inspiring theorem Integer polygons Pythagoras Heron Heptadecagon: true or false Robbins' pentagons Napoleon, geometer of the world
Dossier 3: The Universe of Quadrilaterals
Quadrilaterals are generally presented and classified as subcategories of the parallelogram. This leads to thinking that any general quadrilateral would have no interest. What an error! Very beautiful properties are enjoyed in the most general cases.
Topics covered
Meeting quadrilaterals This is not a square Convex quadrilaterals Circumscriptible quadrilaterals Orthodiagonals Extending to complete
Dossier 4: A World with Multiple Sides
Polygons extend well beyond the strict framework of geometry, with practical or recreational applications. They are found, for example, in architecture or arithmetic. They are naturally the tesserae of many puzzles and subjects of a vast field of mathematical recreations.
Topics covered
When polygons form numbers Pentacles and pentagrams The quadrature of polygons Einstein hat! The single cut theorem The hidden riches of the multiplication table The Castel del Monte The Château de Maulnes The vertex polygon, a polygon at the summit! The Petrie polygon