Outline

# Terry's Maths Collections

## Table of Contents

### It's all about triangles...

- How to reconstruct a quadrilateral farm to a triangular one with the same area?
- Why same areas?
- Why ratio difference is the same?
- Why same areas? (2)
- Why same areas? (3)
- Shortest-perimeter Inscribed Triangle
- Right triangle with median as a geometric mean
- Shortest fence dividing a triangular field into halves
- 4 Centres in a Triangle
- Incircle and Excircles
- Inner/Outer Triangles
- Equilateral Triangle on 3 Concentric Circles
- Why 6 points are concyclic?
- Morley Equilateral Triangles
- Napoleon Equilateral Triangles

### It's all about cyclic quadrilaterals...

### Famous Puzzle Gallery

### Origami

### Proofs without words

- triangular numbers-1
- The Sum of the Cubes of the First N Natural Numbers
- Centered Polygonal Number 中心多邊形數
- The Pythagorean Theorem.
- Proof without words : Area of the triangle
- Fibonacci Numbers and the Golden Spiral - demonstration
- Infinite Geometric Series
- Viviani's Theorem
- Fagnano's Problem
- QM-AM-GM-HM Inequality

### Elegant Solution

### Art Gallery

### Animation