1. Euclidean Geometry
Sangaku
The Regular Pentagon
Constructions With Compass and Straightedge
The Orthocenter and the Euler Line
2. Number Sequences
Some Interesting Number Sequences
The Padovan Sequence
3. Trigonometry
The Arctangent Function
Exact Trigonometric Values
Trigonometric Formulas with Geometry
What Does the Cosine Rule Really Say?
4. Number Theory
Matches and Triangles
Some Remarks from Number Theory
The Farey Fractions
Sums of Powers
5. From the History of Mathematics
Three Classical Problems
The Regular 17-gon
The Lunes of Hippocrates
The Cubic Equation
6. Triangles and Quadrilaterals
The Equilateral Triangle
Two Special Triangles
Quadrilaterals
7. Basic Polynomials and the Hyperbola
The Quadratic Polynomial
The Cubic Polynomial
The Parabola
The Equilateral Hyperbola
8. Dissections and Jigsaw Puzzles
Some Dissections
G. H. Hardy and Srinivasa Ramanujan
Polyominoes and Polycubes
9. Miscellaneous
Complex Numbers and Quaternions
Custard Pie Games
Draw an Arbitrary Triangle
Play With Dice
Mathematical Means
Biography
Jens Cartensen holds a master’s degree in mathematics from the University of Copenhagen and has taught high school and college math for over 40 years. He has extensive experience in publishing textbooks in Denmark and is also the author of several extracurricular books for students and teachers. In the period 1983-2023 he authored 400 problems of the Problem Corner of the Mathematics Teacher’s Association in Denmark and was the editor and main contributor to the small Mathematics Magazine for 15 years.
