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The Sliding Bevel
Construction, woodworking and metalworking require accurate measurements with suitable tools.
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Articles, problems and notes on mathematics. Browse by topic or article type.
Essay
Why Do We Need Algebra? The Mathematician's Bible
A new book by Mansur Gilmullin, The Mathematician’s Bible: Foundations of Higher and Linear Algebra, has appeared. What does it cover, and why do we need algebra?
Problem
The Genoese Lottery Problem
The rules, history and winning probabilities of the Genoese lottery, in which five numbers were drawn from ninety.
Essay
The Thirty-Six Officers Puzzle
Euler’s thirty-six officers puzzle leads to orthogonal Latin squares, a celebrated impossibility result and wide-ranging mathematical applications.
Essay
The History of Algebra, Part II: Elementary Algebra
Continuing the history of algebra: its elementary period, from early equation-solving to the foundations of modern algebra.
Essay
An Algorithm for Extracting Square Roots
A traditional digit-by-digit square-root algorithm, explained through worked examples and justified by the expansion of a squared sum.
Problem
The Grass-Divination Problem
A traditional grass-divination custom becomes a probability problem: what is the chance that six paired blades of grass form one ring?
Essay
MCCME: A Seminar for Mathematics Teachers
Notes from the 155th mathematics teachers’ seminar at the Moscow Center for Continuous Mathematical Education on 30 January 2025.
Essay
The History of Algebra, Part III: Modern Algebra
From Galois and abstract operations to algebraic structures and modern applications, this essay surveys algebra since the mid-19th century.
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Logarithm Tables: Their Evolution
From Napier and Bürgi to Briggs, Vega and Bradis, logarithm tables transformed laborious multiplication and division into simpler operations.
Essay
The History of Algebra, Part I: The Origins of Algebra
The origins of algebra in ancient Egypt and Greece, from practical calculations and false position to geometric algebra and Diophantus’ notation.
Problem
Einstein's Riddle, According to Legend: Five of Everything
The famous zebra puzzle is often attributed to Einstein by legend. Here is the first known published version, with five houses and five sets of clues.
Problem
Lewis Carroll's Five-Bag Puzzle
“A knot!” said Alice. “Oh, do let me help to undo it!” (Lewis Carroll)
Essay
Magnitsky’s Mixing Method
Mixture word problems received considerable attention in early mathematical texts, including Leonty Magnitsky’s Arithmetic.
Essay
Fermat’s Christmas Theorem
The history of mathematics contains many remarkable achievements and problems associated with Pierre de Fermat, its “great amateur”.
Essay
Rachinsky's Sequences
Rachinsky’s identities divide consecutive natural numbers into two groups with equal sums of squares, offering a striking method for mental arithmetic.
Instrument
The Slide Rule: An Ancestor of Modern Computing Devices
The slide rule turns multiplication and division into operations on logarithmic scales and served generations of engineers before pocket calculators.
Essay
The Mathematician's Bible: Higher and Linear Algebra
A new book by Mansur Gilmullin, author of Mathematics with Mansur-abyy: a lifetime of material on the foundations of algebra.
Problem
Cows in a Meadow: A Problem from Newton’s Universal Arithmetic
“In studying the sciences, problems are more useful than rules.” — I. Newton
Essay
Prime Numbers: A History Across the Centuries
“Prime numbers were made to be multiplied”: their story stretches from ancient Greece to modern records and public-key cryptography.
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