Kakeya Conjecture: What is the minimum area required to rotate a needle a full turn?
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22 pages
Geometry
Einstein Tiles and Penrose Tiles: The Intersection of Aperiodic Tiling and Crystallography
What is the largest sofa that can turn a corner? The abyss of the unsolved geometric 'Moving Sofa Problem' that continues to puzzle mathematicians
David Hilbert: The Giant Who Laid the Foundations of Modern Mathematics and His Epic Trajectory
Gabriel Lamé: A Giant Bridging Pure and Applied Mathematics
Adrien-Marie Legendre: The Shadow Giant of Mathematics, Feud with Gauss, and the Portrait Mystery
Carl Friedrich Gauss: Life and Achievements of the Prince of Mathematicians
Gilles Personne de Roberval: Pioneer of Indivisibles and Kinematic Geometry
Euclid: The Father of Geometry and His Great Legacy
Pythagoras: The Intersection of Mathematics and Mysticism
The Genius of Ancient Greece: Life and Mathematical Achievements of Archimedes
Affine and Projective Transformations: The Fusion of Linear Algebra and Geometry behind CG and Perspective
Diverse Proofs of the Pythagorean Theorem: From Geometry and Algebra to Einstein
Euler's Polyhedron Formula: The Magic of Topology Shown by V - E + F = 2
The Möbius Strip and Klein Bottle: A Fascinating World of Surfaces with No 'Inside' or 'Outside'
Geometric Meaning of the Determinant: More Than Just a Formula, It's the 'Volume Scale Factor' and 'Orientation Reversal'
Pick's Theorem: Finding Area Just by Counting Lattice Points
The Ham Sandwich Theorem: Can You Halve 3 Ingredients with One Cut?
The Birth of Non-Euclidean Geometry - The Discovery of "Curved Space" and the Path to the Theory of Relativity
Gauss's Theorema Egregium - A Monumental Milestone in Differential Geometry That Can Also Be Applied to How You Eat Pizza
