https://mklab.gr/ Sat, 12 Sep 2026 11:15:19 +0000 MyBB https://mklab.gr/showthread.php?tid=1908 Tue, 08 Sep 2026 18:22:26 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1908 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

• 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]]> 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

• 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]]> https://mklab.gr/showthread.php?tid=1840 Fri, 04 Sep 2026 03:23:56 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1840
Mathematical Vistas: From a Room with Many Windows
Authors: Peter Hilton, Derek Holton, Jean Pedersen
Publication date: 2002
Publisher: Springer-Verlag New York
Series:Undergraduate Texts in Mathematics

Mathematical Vistas is an accessible collection of largely independent mathematical essays intended to show the creativity, surprise, and pleasure involved in doing mathematics. Rather than developing a single subject systematically like a conventional textbook, the authors explore nine diverse topics, inviting readers to investigate ideas, experiment with examples, and discover mathematical patterns for themselves. It is a companion to their earlier Mathematical Reflections, but can be read entirely independently. 

The topics range widely across elementary but surprisingly deep mathematics. The book discusses mathematical paradoxes and Fermat's Last Theorem, then explores Fibonacci and Lucas numbers and their divisibility properties. It connects paper folding and polyhedron construction with number theory, examines the Four Color Theorem, generalizes binomial coefficients to trinomial and higher-dimensional analogues, studies the ubiquitous Catalan numbers, and investigates symmetry. The final chapter, Parties, develops combinatorial ideas arising from social-group configurations. 

A distinctive feature is the emphasis on active mathematical exploration. Throughout the chapters the authors insert “Breaks”—problems asking readers to stop and work something out before continuing. Many arguments are accessible to strong high-school students and undergraduates, yet the material frequently leads toward genuine research mathematics. Reviewers particularly praised the informal style, geometric illustrations, unusual choice of topics, and the way the authors convey mathematics as a living process of discovery rather than a collection of finished formulas. 

Key topics

• Mathematical paradoxes
  
• Fermat's Last Theorem
  
• Fibonacci and Lucas numbers
  
• Divisibility and number theory
  
• Paper folding and polyhedra
  
• Four Color Theorem
  
• Binomial and trinomial coefficients
  
• Catalan numbers
  
• Symmetry
  
• Combinatorial problems involving groups and “parties” 
  

Key takeaways

1. Elementary mathematics can quickly lead to deep mathematics. Familiar objects such as Fibonacci numbers, binomial coefficients, paper folding, and colored maps open doors to substantial number theory, combinatorics, and geometry.
   
2. The book teaches mathematical thinking more than a fixed syllabus. Readers are repeatedly encouraged to conjecture, test examples, solve problems, and understand why a result should be true.
   
3. It is especially suitable for mathematically curious students and teachers. The independent chapters make it useful for enrichment, math clubs, undergraduate seminars, or simply recreational reading; contemporary reviews specifically recommended it for interested high-school and college students.
   

BOOK]]>
Mathematical Vistas: From a Room with Many Windows
Authors: Peter Hilton, Derek Holton, Jean Pedersen
Publication date: 2002
Publisher: Springer-Verlag New York
Series:Undergraduate Texts in Mathematics

Mathematical Vistas is an accessible collection of largely independent mathematical essays intended to show the creativity, surprise, and pleasure involved in doing mathematics. Rather than developing a single subject systematically like a conventional textbook, the authors explore nine diverse topics, inviting readers to investigate ideas, experiment with examples, and discover mathematical patterns for themselves. It is a companion to their earlier Mathematical Reflections, but can be read entirely independently. 

The topics range widely across elementary but surprisingly deep mathematics. The book discusses mathematical paradoxes and Fermat's Last Theorem, then explores Fibonacci and Lucas numbers and their divisibility properties. It connects paper folding and polyhedron construction with number theory, examines the Four Color Theorem, generalizes binomial coefficients to trinomial and higher-dimensional analogues, studies the ubiquitous Catalan numbers, and investigates symmetry. The final chapter, Parties, develops combinatorial ideas arising from social-group configurations. 

A distinctive feature is the emphasis on active mathematical exploration. Throughout the chapters the authors insert “Breaks”—problems asking readers to stop and work something out before continuing. Many arguments are accessible to strong high-school students and undergraduates, yet the material frequently leads toward genuine research mathematics. Reviewers particularly praised the informal style, geometric illustrations, unusual choice of topics, and the way the authors convey mathematics as a living process of discovery rather than a collection of finished formulas. 

Key topics

• Mathematical paradoxes
  
• Fermat's Last Theorem
  
• Fibonacci and Lucas numbers
  
• Divisibility and number theory
  
• Paper folding and polyhedra
  
• Four Color Theorem
  
• Binomial and trinomial coefficients
  
• Catalan numbers
  
• Symmetry
  
• Combinatorial problems involving groups and “parties” 
  

Key takeaways

1. Elementary mathematics can quickly lead to deep mathematics. Familiar objects such as Fibonacci numbers, binomial coefficients, paper folding, and colored maps open doors to substantial number theory, combinatorics, and geometry.
   
2. The book teaches mathematical thinking more than a fixed syllabus. Readers are repeatedly encouraged to conjecture, test examples, solve problems, and understand why a result should be true.
   
3. It is especially suitable for mathematically curious students and teachers. The independent chapters make it useful for enrichment, math clubs, undergraduate seminars, or simply recreational reading; contemporary reviews specifically recommended it for interested high-school and college students.
   

BOOK]]> https://mklab.gr/showthread.php?tid=1358 Sun, 26 Jul 2026 04:09:13 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1358 The Mathematics of Various Entertaining Subjects: Research in Recreational Math 
BY Jennifer Beineke and Jason Rosenhouse

Summary

The Mathematics of Various Entertaining Subjects: Research in Recreational Math, edited by Jennifer Beineke and Jason Rosenhouse, explores how playful problems, puzzles, and games can lead to serious mathematical discoveries. The book presents research articles showing the deep connections between recreational mathematics and advanced areas such as combinatorics, graph theory, topology, probability, and coding theory. 

Topics include mathematical approaches to maze design, crossword puzzles, the Tower of Hanoi, card games such as SET, coin-weighing problems, flexagons, poker, and new versions of tic-tac-toe. The collection demonstrates that seemingly simple recreational activities can reveal powerful mathematical structures and inspire genuine research, continuing a tradition where puzzles and games have contributed to major developments in mathematics, such as probability theory and combinatorics. It is aimed at mathematicians, students, and enthusiasts who want to see the creativity, elegance, and surprising depth hidden within entertaining mathematical challenges.

BOOK]]> The Mathematics of Various Entertaining Subjects: Research in Recreational Math 
BY Jennifer Beineke and Jason Rosenhouse

Summary

The Mathematics of Various Entertaining Subjects: Research in Recreational Math, edited by Jennifer Beineke and Jason Rosenhouse, explores how playful problems, puzzles, and games can lead to serious mathematical discoveries. The book presents research articles showing the deep connections between recreational mathematics and advanced areas such as combinatorics, graph theory, topology, probability, and coding theory. 

Topics include mathematical approaches to maze design, crossword puzzles, the Tower of Hanoi, card games such as SET, coin-weighing problems, flexagons, poker, and new versions of tic-tac-toe. The collection demonstrates that seemingly simple recreational activities can reveal powerful mathematical structures and inspire genuine research, continuing a tradition where puzzles and games have contributed to major developments in mathematics, such as probability theory and combinatorics. It is aimed at mathematicians, students, and enthusiasts who want to see the creativity, elegance, and surprising depth hidden within entertaining mathematical challenges.

BOOK]]> https://mklab.gr/showthread.php?tid=1232 Tue, 21 Jul 2026 04:27:05 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1232 Math on Trial: How Numbers Get Used and Abused in the Courtroom 
BY  Leila Schneps

Summary

Math on Trial: How Numbers Get Used and Abused in the Courtroom explores how mathematical and statistical errors have influenced some of the most famous legal cases in modern history. Written by mathematicians Leila Schneps and Coralie Colmez, the book presents ten real court cases in which misunderstandings of probability, statistics, and mathematical reasoning contributed to wrongful convictions, flawed investigations, or unjust verdicts. 

Each chapter introduces a common mathematical fallacy before explaining how it affected a specific case, including those involving Sally Clark, Amanda Knox, Charles Ponzi, Lucia de Berk, and the Dreyfus Affair. Rather than requiring advanced mathematical knowledge, the authors explain complex ideas in an accessible way, demonstrating how seemingly simple numerical mistakes can have life-changing consequences. 

Blending true crime, legal history, and mathematics, the book highlights the importance of critical thinking and statistical literacy, arguing that numbers are only as reliable as the people who interpret them. It ultimately serves as a compelling reminder that mathematical reasoning must be applied carefully, especially when justice and human lives are at stake. 

BOOK]]> Math on Trial: How Numbers Get Used and Abused in the Courtroom 
BY  Leila Schneps

Summary

Math on Trial: How Numbers Get Used and Abused in the Courtroom explores how mathematical and statistical errors have influenced some of the most famous legal cases in modern history. Written by mathematicians Leila Schneps and Coralie Colmez, the book presents ten real court cases in which misunderstandings of probability, statistics, and mathematical reasoning contributed to wrongful convictions, flawed investigations, or unjust verdicts. 

Each chapter introduces a common mathematical fallacy before explaining how it affected a specific case, including those involving Sally Clark, Amanda Knox, Charles Ponzi, Lucia de Berk, and the Dreyfus Affair. Rather than requiring advanced mathematical knowledge, the authors explain complex ideas in an accessible way, demonstrating how seemingly simple numerical mistakes can have life-changing consequences. 

Blending true crime, legal history, and mathematics, the book highlights the importance of critical thinking and statistical literacy, arguing that numbers are only as reliable as the people who interpret them. It ultimately serves as a compelling reminder that mathematical reasoning must be applied carefully, especially when justice and human lives are at stake. 

BOOK]]> https://mklab.gr/showthread.php?tid=1159 Thu, 16 Jul 2026 17:57:57 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1159
What's the Use?: The Unreasonable Effectiveness of Mathematics  
BY Professor Ian Stewart

Summary

Ian Stewart’s What’s the Use?: The Unreasonable Effectiveness of Mathematics explores the surprising ways mathematics shapes the modern world and challenges the common belief that math is only about abstract theories and classroom exercises. Stewart explains that many mathematical discoveries, even those that seemed useless at first, later became essential for technology, science, medicine, and everyday life. 

Through engaging examples, he shows how mathematics influences areas such as satellite navigation, computer security, medical procedures, voting systems, and digital technologies. The book reveals that mathematics often works quietly behind the scenes, providing the hidden structures that make modern society possible. Stewart’s main message is that mathematics is not just a tool for calculation but a powerful way of understanding and transforming the world around us.


BOOK PAGE]]>
What's the Use?: The Unreasonable Effectiveness of Mathematics  
BY Professor Ian Stewart

Summary

Ian Stewart’s What’s the Use?: The Unreasonable Effectiveness of Mathematics explores the surprising ways mathematics shapes the modern world and challenges the common belief that math is only about abstract theories and classroom exercises. Stewart explains that many mathematical discoveries, even those that seemed useless at first, later became essential for technology, science, medicine, and everyday life. 

Through engaging examples, he shows how mathematics influences areas such as satellite navigation, computer security, medical procedures, voting systems, and digital technologies. The book reveals that mathematics often works quietly behind the scenes, providing the hidden structures that make modern society possible. Stewart’s main message is that mathematics is not just a tool for calculation but a powerful way of understanding and transforming the world around us.


BOOK PAGE]]> https://mklab.gr/showthread.php?tid=1149 Thu, 16 Jul 2026 03:08:07 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1149 The Penguin Book of Curious and Interesting Mathematics 
BY [DAVID Wells]

Summary

The Penguin Book of Curious and Interesting Mathematics by David G. Wells is an engaging, lighthearted anthology that celebrates the quirky, human side of mathematics across history. Rather than focusing on dry textbooks or complex proofs, Wells curates a delightful "minestrone" of eccentric anecdotes, historical trivia, puzzles, and jokes centered around the brilliant and often bizarre minds who shaped the discipline. 

Readers will find stories ranging from Isaac Newton's thoughts on chance and chaos to the life of Pythagoras, alongside historical oddities like legal attempts to redefine the value of pi or mathematical references hidden in the Bible. Wells also explores the strange ways mathematics intersects with other aspects of life—including madness, misogyny, the military, and even the bizarre measuring habits of old explorers—proving that while numbers are logical, the people who study them are anything but.


BOOK]]> The Penguin Book of Curious and Interesting Mathematics 
BY [DAVID Wells]

Summary

The Penguin Book of Curious and Interesting Mathematics by David G. Wells is an engaging, lighthearted anthology that celebrates the quirky, human side of mathematics across history. Rather than focusing on dry textbooks or complex proofs, Wells curates a delightful "minestrone" of eccentric anecdotes, historical trivia, puzzles, and jokes centered around the brilliant and often bizarre minds who shaped the discipline. 

Readers will find stories ranging from Isaac Newton's thoughts on chance and chaos to the life of Pythagoras, alongside historical oddities like legal attempts to redefine the value of pi or mathematical references hidden in the Bible. Wells also explores the strange ways mathematics intersects with other aspects of life—including madness, misogyny, the military, and even the bizarre measuring habits of old explorers—proving that while numbers are logical, the people who study them are anything but.


BOOK]]> https://mklab.gr/showthread.php?tid=846 Sat, 04 Jul 2026 16:30:15 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=846 Who's #1?
by CARL MEYER

Summary

The post reviews the book “Who’s #1? The Science of Rating and Ranking,” which explores the mathematics behind how we rank things in everyday life—like Google search results, Netflix recommendations, sports teams, and even Amazon products. It explains that the book breaks down different ranking algorithms, often using sports (especially college football) as a running example to show how these systems work and how they can be adjusted depending on what you want to emphasize, such as recent performance or tie-breaking rules. 

It also looks at more advanced ideas like combining multiple ranked lists into a single “best” list and measuring how different rankings compare. While the book is praised for being rich in examples and accessible to readers with some linear algebra background, the reviewer notes a minor criticism regarding its treatment of Arrow’s Impossibility Theorem. Overall, the post presents the book as a fun and practical bridge between abstract math and real-world decision-making.

BOOK]]> Who's #1?
by CARL MEYER

Summary

The post reviews the book “Who’s #1? The Science of Rating and Ranking,” which explores the mathematics behind how we rank things in everyday life—like Google search results, Netflix recommendations, sports teams, and even Amazon products. It explains that the book breaks down different ranking algorithms, often using sports (especially college football) as a running example to show how these systems work and how they can be adjusted depending on what you want to emphasize, such as recent performance or tie-breaking rules. 

It also looks at more advanced ideas like combining multiple ranked lists into a single “best” list and measuring how different rankings compare. While the book is praised for being rich in examples and accessible to readers with some linear algebra background, the reviewer notes a minor criticism regarding its treatment of Arrow’s Impossibility Theorem. Overall, the post presents the book as a fun and practical bridge between abstract math and real-world decision-making.

BOOK]]> https://mklab.gr/showthread.php?tid=841 Sat, 04 Jul 2026 15:30:18 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=841 X and the City: Modeling Aspects of Urban Life
by John Adam

Summary

The book “X and the City: Modeling Aspects of Urban Life” by John A. Adam is a friendly, non-technical introduction to how mathematics can be used to understand everyday life in cities. It explores real-world urban questions in an accessible way, such as how many shops or services a city of a given size can support, how traffic flows through roads and tunnels, how to model congestion and traffic lights, and even the chances of rare events like an asteroid hitting a city. 

Instead of abstract theory, the author turns each topic into a story-driven problem, showing how simple mathematical models (from basic calculus up to differential equations) can explain patterns in urban life. The overall tone is playful and curious, making it feel like a guided mathematical walk through a living, breathing city.

BOOK]]> X and the City: Modeling Aspects of Urban Life
by John Adam

Summary

The book “X and the City: Modeling Aspects of Urban Life” by John A. Adam is a friendly, non-technical introduction to how mathematics can be used to understand everyday life in cities. It explores real-world urban questions in an accessible way, such as how many shops or services a city of a given size can support, how traffic flows through roads and tunnels, how to model congestion and traffic lights, and even the chances of rare events like an asteroid hitting a city. 

Instead of abstract theory, the author turns each topic into a story-driven problem, showing how simple mathematical models (from basic calculus up to differential equations) can explain patterns in urban life. The overall tone is playful and curious, making it feel like a guided mathematical walk through a living, breathing city.

BOOK]]>