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Percentages and Their Companions: %, Percentage Points and Basis Points
Percentages, percentage points and basis points measure different kinds of change; practical examples show how to distinguish them.
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Articles, problems and notes on mathematics. Browse by topic or article type.
Instrument
The Vernier Scale
A vernier is an auxiliary scale that allows fractions of a main scale division to be read more precisely; its history links Nunes, Vernier and Avicenna.
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John Horton Conway: The Man Who Played with Mathematics
John Horton Conway, creator of the Game of Life, made major contributions to group theory, games, surreal numbers and recreational mathematics.
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What Is Life? A Game!
John Horton Conway’s Game of Life uses simple cellular-automaton rules to generate a remarkable diversity of patterns, attracting researchers and enthusiasts for decades.
Instrument
The Pocket Calculator
From Soviet pocket calculators to scientific and programmable models: the history, operating logic and educational uses of the electronic calculator.
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Mathematics Education at School and University: Content and Methods
On 26–28 September, Pitirim Sorokin Syktyvkar State University hosted the 43rd international seminar on mathematics education.
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Farey Sequences
Farey sequences form a family of finite sets of rational numbers with distinctive and mathematically beautiful properties.
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Where Mathematics, Teaching and Economics Meet: Similarity, Exams, Functional Literacy and Saving Paper
Paper formats connect geometric similarity with practical exam tasks, mathematical literacy and economical printing.
Instrument
The Telescopic Alidade
The telescopic alidade measures height differences, distances and vertical angles and plots survey directions on a plane table.
Problem
Kirkman's Schoolgirl Problem: A Challenge in Combinatorics
Arranging fifteen schoolgirls in rows of three for seven days led to a famous combinatorial problem and the study of combinatorial designs.
Essay
The Plane Table
Homothety in practical surveying: the plane table transfers directions and distances from the terrain onto a drawing.
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The Kiss Precise: The Descartes–Soddy Formula
Frederick Soddy (1877–1956), an English radiochemist and Fellow of the Royal Society from 1910, received the Nobel Prize in Chemistry in 1921.
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The Pentagram
The Pythagoreans’ five-pointed star connects the golden ratio, classical means and a long history of symbolic uses.
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Stepan Yakovlevich Rumovsky (1734–1812)
Euler's pupil Stepan Rumovsky helped shape mathematics, astronomy and education in Russia, from the Academy of Sciences to Kazan University.
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Crises in the Development of Mathematics
Incommensurability, infinitesimals and set theory frame a discussion of crises and the foundations of mathematics.
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The Art of Computer Programming: Donald Knuth
Marking Donald Knuth's 85th birthday: mathematics, algorithms, The Art of Computer Programming and the creation of TeX.
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Pythagorean Arithmetic: Perfect Numbers
Why is 6 a perfect number? Explore proper divisors, the Euclid–Euler theorem, Mersenne primes and the enduring mystery of odd perfect numbers.
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An Extraordinary Phenomenon: Andrey Nikolaevich Kolmogorov, 1903–1987
On the 120th anniversary of Andrey Nikolaevich Kolmogorov: his mathematical discoveries, scholarship, teaching and influence on school education.
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I Made the Pursuit of Knowledge My Trade
On the 975th anniversary of Omar Khayyam (1048–1131): the astronomer, mathematician, philosopher and poet whose quatrains made him immortal.
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Leonardo da Vinci: A Fountain of Ideas
Leonardo da Vinci was a brilliant Renaissance painter and an extraordinarily gifted inventor whose interests ranged across mathematics, mechanics, anatomy and natural science.
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