4. Geometry and Measures - Mathematics

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Contents

Properties and Constructions

Enrichment - Polygons and Polyhedra

Enrichment - Pythagorean Theorem

Enrichment - Tiling Theory

Properties and Constructions

PROPERTIES AND CONSTRUCTIONS I – AQA GCSE (8300): HIGHER TIER

Terms and Notation – G1

Prof. Jason Lotay, University of Oxford

PROPERTIES AND CONSTRUCTIONS I – AQA GCSE (8300): HIGHER TIER

Ruler and Compass Construction – G2

Prof. Jason Lotay, University of Oxford

PROPERTIES AND CONSTRUCTIONS I – AQA GCSE (8300): HIGHER TIER

Angles – G3

Prof. Jason Lotay, University of Oxford

PROPERTIES AND CONSTRUCTIONS I – AQA GCSE (8300): HIGHER TIER

Triangles – G4, G5, G6

Prof. Jason Lotay, University of Oxford

PROPERTIES AND CONSTRUCTIONS I – AQA GCSE (8300): HIGHER TIER

Quadrilaterals – G4, G6

Prof. Jason Lotay, University of Oxford

PROPERTIES AND CONSTRUCTIONS I – AQA GCSE (8300): HIGHER TIER

Basic Proofs and the Golden Ratio – G6

Prof. Jason Lotay, University of Oxford

Enrichment - Polygons and Polyhedra

2D POLYGONS

Why 2-Dimensional Polygons?

Prof. Satyan Devadoss, University of San Diego

2D POLYGONS

Breaking Polygons into Triangles: Diagonalization and Triangulation

Prof. Satyan Devadoss, University of San Diego

2D POLYGONS

Polygons in Sensors and Security

Prof. Satyan Devadoss, University of San Diego

2D POLYGONS

Congruency, Similarity, and Scissors Congruency of Polygons

Prof. Satyan Devadoss, University of San Diego

2D POLYGONS

3-Dimensional Polyhedra

Prof. Satyan Devadoss, University of San Diego

3D POLYHEDRA

Regular 2-Dimensional Polygons

Prof. Satyan Devadoss, University of San Diego

3D POLYHEDRA

Regular 3-Dimensional Polyhedra

Prof. Satyan Devadoss, University of San Diego

3D POLYHEDRA

The Platonic Solids

Prof. Satyan Devadoss, University of San Diego

3D POLYHEDRA

Adding the Fourth Dimension

Prof. Satyan Devadoss, University of San Diego

3D POLYHEDRA

Regular 4-Dimensional Polytopes and Beyond

Prof. Satyan Devadoss, University of San Diego

Enrichment - Pythagorean Theorem

PYTHAGORAS: THE REAL STORY

The Pythagorean Cult

Dr Piers Bursill-Hall, University of Cambridge

PYTHAGORAS: THE REAL STORY

Pythagorean Beliefs

Dr Piers Bursill-Hall, University of Cambridge

PYTHAGORAS: THE REAL STORY

The Pythagoreans Did Not Discover Or Prove the Pythagorean Theorem

Dr Piers Bursill-Hall, University of Cambridge

PYTHAGORAS: THE REAL STORY

A Visual Proof of the Pythagorean Theorem

Dr Piers Bursill-Hall, University of Cambridge

PYTHAGORAS: THE REAL STORY

The Tunnel of Eupalinos

Dr Piers Bursill-Hall, University of Cambridge

PYTHAGORAS: THE REAL STORY

The Pythagoreans Did Not Discover Irrational Numbers

Prof. Kevin Buzzard, Imperial College London

PYTHAGORAS: THE REAL STORY

Why Do We Have the Wrong Story?

Dr Piers Bursill-Hall, University of Cambridge

Enrichment - Tiling Theory

INTRODUCTION TO TILING THEORY

What is Tiling Theory?

Prof. Colin Adams, Williams College

INTRODUCTION TO TILING THEORY

Generating Monohedral Tilings and Tiling Symmetries

Prof. Colin Adams, Williams College

INTRODUCTION TO TILING THEORY

Monomorphic Tilings and Random Tilings

Prof. Colin Adams, Williams College

INTRODUCTION TO TILING THEORY

Uniform Tilings and Coronas

Prof. Colin Adams, Williams College

INTRODUCTION TO TILING THEORY

Applications of Aperiodic Tilings to Quasicrystals

Prof. Colin Adams, Williams College