09-08-2026, 03:22 PM
Mathematical Tidbits
Author: Jens Cartensen
Publication date: September 2026
Publisher: A K Peters/CRC Press, an imprint of Taylor & Francis
ISBN: 9781041288725
Mathematical Tidbits is a collection of short, largely self-contained mathematical essays designed to present elegant, surprising, and entertaining ideas without requiring advanced prerequisites. Rather than developing one subject systematically like a conventional textbook, the book moves across Euclidean geometry, number sequences, trigonometry, number theory, the history of mathematics, polynomials, dissections, combinatorial puzzles, probability, and complex numbers. Topics include Japanese sangaku geometry, the regular pentagon, compass-and-straightedge constructions, the Euler line, the Padovan sequence, exact trigonometric values, Farey fractions, sums of powers, the classical construction problems, the regular $17$-gon, the lunes of Hippocrates, cubic equations, polyominoes, quaternions, dice problems, and mathematical means.
The emphasis is on discovering interesting relationships rather than on formal theory. Individual chapters function as mathematical “capsules”: a familiar problem or object is introduced and then developed in directions that may produce an unexpected identity, geometric interpretation, construction, or generalization. Problems and solutions are incorporated throughout, and the book makes extensive use of colour illustrations. According to the publisher, the mathematical level is accessible enough for interested non-specialists while still containing observations that experienced mathematicians may find surprising.
For a secondary-school mathematics teacher, the book looks particularly useful because many subjects lie close to the school curriculum while going considerably beyond routine exercises. Sections such as What Does the Cosine Rule Really Say?, exact trigonometric values, Farey fractions, geometric constructions, special triangles, dissections and number sequences could readily provide enrichment problems, mathematics-club material, classroom investigations, or ideas for talented students. Cartensen brings more than forty years of high-school and college teaching experience and authored hundreds of problems for the Danish Mathematics Teacher's Association, which helps explain the book's strong problem-solving orientation.
Key takeaways
BOOK
Author: Jens Cartensen
Publication date: September 2026
Publisher: A K Peters/CRC Press, an imprint of Taylor & Francis
ISBN: 9781041288725
Mathematical Tidbits is a collection of short, largely self-contained mathematical essays designed to present elegant, surprising, and entertaining ideas without requiring advanced prerequisites. Rather than developing one subject systematically like a conventional textbook, the book moves across Euclidean geometry, number sequences, trigonometry, number theory, the history of mathematics, polynomials, dissections, combinatorial puzzles, probability, and complex numbers. Topics include Japanese sangaku geometry, the regular pentagon, compass-and-straightedge constructions, the Euler line, the Padovan sequence, exact trigonometric values, Farey fractions, sums of powers, the classical construction problems, the regular $17$-gon, the lunes of Hippocrates, cubic equations, polyominoes, quaternions, dice problems, and mathematical means.
The emphasis is on discovering interesting relationships rather than on formal theory. Individual chapters function as mathematical “capsules”: a familiar problem or object is introduced and then developed in directions that may produce an unexpected identity, geometric interpretation, construction, or generalization. Problems and solutions are incorporated throughout, and the book makes extensive use of colour illustrations. According to the publisher, the mathematical level is accessible enough for interested non-specialists while still containing observations that experienced mathematicians may find surprising.
For a secondary-school mathematics teacher, the book looks particularly useful because many subjects lie close to the school curriculum while going considerably beyond routine exercises. Sections such as What Does the Cosine Rule Really Say?, exact trigonometric values, Farey fractions, geometric constructions, special triangles, dissections and number sequences could readily provide enrichment problems, mathematics-club material, classroom investigations, or ideas for talented students. Cartensen brings more than forty years of high-school and college teaching experience and authored hundreds of problems for the Danish Mathematics Teacher's Association, which helps explain the book's strong problem-solving orientation.
Key takeaways
- Breadth rather than specialization: the book samples many areas of elementary and recreational mathematics.
- Problem-solving focused: mathematics is explored through concrete problems, constructions and unexpected connections rather than long theoretical developments.
- Very suitable for teachers: many topics can be adapted directly into enrichment activities for secondary-school students.
- Visual and accessible: self-contained essays and extensive illustrations make it suitable for browsing rather than necessarily reading sequentially.
BOOK
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