List

Articles about mathematics

Divisibility Tests
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Divisibility tests

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

All about Infinity
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All about infinity

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.
Ding Dong Bell
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Ding dong bell

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
The random world
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The random world

Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.
The Best Card Trick?
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The best card trick?

Age
11 to 16
Challenge level
filled star empty star empty star

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Tournament Scheduling
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Tournament scheduling

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
Whole Number Dynamics I
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Whole number dynamics I

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

Links and Knots
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Links and knots

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.
The Chinese Remainder Theorem
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The Chinese remainder theorem

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."

Keeping it safe and quiet
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Keeping it safe and quiet

Simon Singh describes PKC, its origins, and why the science of code making and breaking is such a secret occupation.
Mouhefanggai
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Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
What are Complex Numbers?
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What are complex numbers?

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.
Euler's Formula
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Euler's formula

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.
Where do we get our feet wet?
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Where do we get our feet wet?

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
Fractional Calculus I
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Fractional calculus I

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.

The why and how of substitution
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The why and how of substitution

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

How many geometries are there?
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How many geometries are there?

An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.
Mathematics In the Financial Markets
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Mathematics in the financial markets

Financial markets mean the business of trading risk. The article describes in simple terms what is involved in this trading, the work people do and the figures for starting salaries.
Infinite Continued Fractions
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Infinite continued fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
Conic Sections
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Conic sections

The interplay between the two and three dimensional Euclidean geometry of conic sections is explored in this article. Suitable for students from 16+, teachers and parents.
Public Key Cryptography
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Public key cryptography

An introduction to coding and decoding messages and the maths behind how to secretly share information.