Why does 0.99999... = 1?
3.1415... : KEY 174-178, PSAUS 15, 150-152,
LUCKY 143-147, MM2 89-94,
EQEA 24, ASAS 52-57
4 Colour Map Theorem: Four Colour Map Theorem
9: KEY 151-163
11: Can I divide the world into football teams? EQEA 14, When will a number divide by 11?
12: 12 Coin Balance Problem
13: fear of KEY 78-89
37: KEY 37
1089: MM1 78-80, 1089 times table EQEA 15-16, 1089
2018: 2018 The Nine-Bead Necklace Number
4 4's: Sunny's Four 4's Challenge
Abacus: MM1 33-34
Acceleration: PSAUS 46-54
Accuracy: measurement DMEAS 27
Activities: see our Teacher Resources page
Addition: SOS 22-34, AWAR 19-31
Algebra: PHX (entire book), card trick MM1 116-124
Alternate Segment: The Alternate Segment Theorem & Proof
Amicable numbers: KEY 148-150
Angles: ASAS 16-23, DMEAS 115-126, MM1 73-78, opposite, corresponding SAVSH 16-17, very small FANG 138-158
Angstrom: DMEAS 21
Annulus: formula PSAUS 163-165, The area of an ANULUS
Archimedes: BBB 29-40, principle DMEAS 135-144, MM1 10, DMEAS 150-157, sphere formula PSAUS 167-170
Arcsecond: FANG 138-139
AREA: formulas PSAUS 10, 116-142, measuring ASAS 75-90, DMEAS 92-110, Area calculator
Articles: Stories from "The Week" that amused us, The Cicadas 17-year Life Cycle, The Al-Gebra Movement, Cool Greek Maths Geeks
Astonomical Unit (au): FANG 155
Averages: MANDV 124-156
Babylonians: KEY 128
Base 8: KEY 126-127
Bear Hunter Puzzle: SAVSH 63-65, The Bear Hunter Puzzle
Bearings and navigation: FANG 181-196
Bell ringing: LUCKY 99-103
Big numbers: MM1 130-135, EQEA 119-128
Binary: KEY 130-133, code CODES 18-24,
Birthdays: BBB 115-116, EQEA 100-105, chances of sharing LUCKY 125-128, What are the chances of 366 strangers all having different birthdays?, The Day of the Huntrodds!
Bisecting lines and angles: MM2 113-119, lines SAVSH 22-26, angles SAVSH 26-27
Blue moon: EQEA 44
Brackets: PHX 22-24, AWAR 167-168
Buoyancy: DMEAS 146-149
Caesar Shift Code: Caesar Shift
Cake: dividing fairly SAVSH 51-60
Calculator: getting sin, cos, tan values FANG 75-87, tricks MOM 11-38
Calculators (online): Area calculator, LCD and HCF, Prime Number calculator,
Time calculator,
Quadratic calculator, The Factoriser Calculator.
Calculus: A bit of Calculus!. There is an introduction and explanation in "Newton and His Falling Apple" by Kjartan Poskitt. differential calculus 56-63, integral calculus 92-94.
Calendar: BBB 109-116, EQEA 49-57, Babylonian Julian Gregorian DMEAS 159, tricks MOM 58-62, The Calendar Trick
Cancelling fractions: MANDV 56-63
Cards (playing cards): chances LUCKY 128-136, chances MMoE 75-77, tricks MOM 63-99, algebra trick MM1 116-124, The Chances of Card Hands, How many different ways can you put a pack of cards in order?
Centred Hexagon Numbers: KEY 60-62, PSAUS 19
Chance: LUCKY (whole book), MMoE 81-84, The Chances of Card Hands, The National Lottery Odds The Day of the Huntrodds!
Chaos Maths: Sierpinski's Triangle MMoE 80
Chess board curiosities: MMoE 7-8, 85-87, chess and dominoes MM2 14-23, How many squares on a chess board?, The Knight's Move Magic Square, The Eight Queens Chess Puzzle, The Chess Board Illusion
Kjartan Poskitt's Fun Maths Videos
Chocolate bar: how many snaps to break EQEA 78
Chords (of circles): SAVSH 106-113, PSAUS 155
Chunking: SOS 116-117
Cicidas: MMoE 17, The Cicadas 17-year Life Cycle
CIRCLES: ASAS 49-57, SAVSH 100-120, PSAUS 152-157, The Names of Bits of Circles Quiz, How to find the centre of a circle using a book, How to make a Circle into a Square
Clock arithmetic: EQEA 31-36
Clocks: MM1 60-71
Codes: CODES (whole book), Secrets of Codes
Coefficients: PHX 12, Pascal coefficients PHX 100-107
Coin tossing: LUCKY 18-23, 40-43, 44-60, 63-66, 68, 70-77, MMoE 73-74
Coin Tricks/Problems: MOM 114-132, DBB 52-53, 82, The Coin Pyramid (Tower of Hanoi), The 6 Coin Circle Problem, The Twelve Coin Balance Problem (and solution)
Combinations: LUCKY 78-103, PSAUS 106-108, The Unknown (Combinations) Formula
Compass: bearings and navigation FANG 181-196
Compasses: circles, bisecting lines and angles MM2 111-119
Cone: volume of cone, area of sloping side PSAUS 172 What is the volume of a cone?
Conversions: PSAUS 195, angles dms calculator button FANG 141
Conway calendar: EQEA 56-57
Co-ordinates: PHX 128-142
Cos: FANG 67-68, 60º, 0º, 90º, 45º FANG 93, cosine formula FANG 119-123
Crescent areas: PSAUS 158-161
Cube (solid): formulas PSAUS 10, 143-146, the 11 nets EQEA 81, The Magical Self-Assembling Cube!
Cube (x3): KEY 57-60, curve on graphs PHX 142
Cube Number Triangles
Squared Triangle and Cube Numbers
Cyclic Quadrilateral: SAVSH 103-105
Cycloid: MMoE 45-47
Day of Week algorithm: PSAUS 95-100
Decimal fractions: SOS 172-178, MANDV 100-111
Decimal point: SOS 160-165, AWAR 163
Degree (angle measurement): ASAS 20-21
Density: DMEAS 145-146, PSAUS 201
Diagonals: PSAUS rectangle 10, 13, polygons 123, 124, cuboids 144, Diagonals of Polygons (with proof)
Dice: LUCKY 23-25, 104-125, SAVSH 128-133, MMoE 78, puzzle DBB 100-102, The Devils Dice Puzzle
Kjartan Poskitt's Fun Maths Videos
Difference of two squares: KEY 50-52, PHX 108-110
Dimension 1D 2D 3D: MMoE 50-51, MM2 33-43, 3D Noughts and Crosses Game
Divine Proportion (or Golden Ratio): KEY 26-31, MMoE 54-55
Division: SOS 104-132, AWAR 107-134 When will numbers divide by 7,11,13? When will numbers divide by 1-10?
Dms: calculator button FANG 141
Dodecahedron: PSAUS 149, SAVSH 121, 127, 131, 135, make MOM 181-186,
Dodecahedron page
Dominoes: BBB 59-75, MM2 13-23
Doubling the cube: MMoE 33-35.
Dragon Curve: MOM 157-162
Drawing: triangles FANG 38-45
e = 2.71828182845904523536... : KEY 178-183, PSAUS 92, The Growth Formula and Elvis Impersonators
Egg: how to draw MMoE 37
Egyptian fractions: MANDV 86-87
Einstein, Albert: PSAUS 65, 69
Ellipses: ASAS 185-201, SAVSH 137-147, how to draw SAVSH 141-143, formulas PSAUS 180-182, The Area of an Ellipse and Volume of Ellipsoids, The Ellipse Page including how to find the centre and foci
Elvis Presley: 2043 - The Year That We All Turn Into ELVIS!
Equations: PHX 19-45, quadratic PHX 56-66, simultaneous PHX 147-156, names of different types MM1 94,
Equilateral triangle: SAVSH 31, how to draw with ruler and compasses SAVSH 74 how to fold from paper SAVSH 96
Eratosthenes: Sieve of Eratosthenes MMoE 14, Circumference of the Earth MMoE 37, Sieve of Eratosthenes
Estimating: AWAR 153-162
Euclid: BBB 28-29
Euler: solids formula SAVSH 123, e,i,PI formula KEY 186, Euler's Formula and Euler's Identity
Exam tips: GCSE Slips and Tips (exam help)
Expanding (brackets): PHX 48-52
Factorial: AWAR 166-167, LUCKY 79-81
Factorising: algebra PHX 48-52, into prime factors MANDV 45-48, 53-55, The Factoriser Calculator
Facts (pathetic): KEY 9-16, 191-192, The Most Pathetic Facts in Maths
February 30th: EQEA 52
Fermat's Last Theorem: KEY 66-70
Fibonacci: MMoE 56-60, KEY 17-41, Fibonacci trick KEY 40-41, PHX 78, formula PSAUS 203, Fibonacci and Nature
Finger Times Tables: KEY 119-122, Finger Times Tables
Fixed point theorem: MMoE 67
Flexagons: MOM 100-113, How to make a Triflexagon video version, How to make Flexagons step by step version
Four 4's: Sunny's Four 4's Challenge
Four colour map theorem: MMoE 68-69, Four Colour Map Theorem
Formulas: PSAUS whole book, EQEA 23, The Unknown Formula
Fortune Telling with numbers: KEY 71-76
Fractal: MOM 162
Fractions: SOS 141-191, MANDV whole book, AWAR 112-114,
Friday 13th: EQEA 55-56
Games: chances of various results in card and board games MMoE 81-84
G.C.S.E Slips and Tips
g Gravity: PSAUS 55, 63. For a lot more information on gravity and forces, see "Isaac Newton and His Apple" by Kjartan Poskitt 69-85, 154-157
Geometry: Catriona Shearer's Gorgeous Geometry Puzzles!
Geometry set: FANG 12-19, ASAS 24-34
Giant people-eating spider: why you can't get one EQEA 86-90
Gigameter: DMEAS 48
Golden Ratio: KEY 26-31, MMoE 54-55
Golomb Rulers: MMoE 48-49, How a Golomb Ruler can make you famous for ever
Gradients (on graphs): PHX 134
Graham's number: EQEA 127
Graphs: x and y axis and how to plot for equations PHX 132-143
HCF (Highest Common Factor): MANDV 52, LCD and HCF calculator
Hemisphere: PSAUS 171
Hexagon: how to draw SAVSH 73, how to fold from paper SAVSH 97, tessalation SAVSH 85,
Horizon: how far away? EQEA 37-41
Huntrodds Day: Sept 19th
Hurricanes: Hurricane measurements, speed, strength and names
Hypotenuse: FANG 60
i : KEY 183-186, square root of i The Research Lab
Icosahedron: PSAUS 149, SAVSH 121, 125, 127, 131
Illusion: MM2 43, Illusions Home Page
Imperial units: DMEAS 30-45
Infinity: KEY 7-9, 188-190
Inscribed circle: PSAUS 118
INT function (integer division): PSAUS 97
Interest (money): PSAUS 82-94.
International date line: MMoE 27-28
Irrational numbers: KEY 164-173
Isosceles triangle: SAVSH 11, 31-32
Jokes: The Murderous Maths Jokes Page
Kaprekar: KEY 115
Kepler: PSAUS 62
K-Puzz Logic Puzzles: K-Puzz Page
Kjarposko Puzzles: KAK, The Dreaded Kjarposkos
LCD or LCM (Lowest Common Denominator / Multiple): MANDV 64-73, 78-80, LCD and HCF calculator
Light year: FANG 155-156, DMEAS 21, EQEA 62
Line, area, volume: MM2 24-54
Locus: SAVSH 21-22
Logic Problems: DBB, how to make a liar tell the truth EQEA 64-68, Dolly's Rush Hour, Luigi's Outside Table
Long Division: SOS 117-130, AWAR 123-126,
Lottery: LUCKY 93-94, The National Lottery Odds
Lucky numbers: KEY 76-77
Magic Squares: MOM 48-62, MM1 103-106, How to make 5x5 and 7x7 Magic Squares, How to make 4x4 Magic Squares
Magic Tricks: MOM, A few tricks from The Magic Of Maths
Mathematicians: MM1 81-97
Mean: averages MANDV 124-156
Measurements: DMEAS whole book, MM2 44-54
Median: MANDV 146-149
Mersenne Primes: KEY 100-103, 142-144 The Research Lab
Metric System: DMEAS 45-51, prefixes EQEA 58-60
Mirror numbers: MM2 107-108
Mobius strip: BBB 96-100, MM2 74-80, MMoE 40-41,
Kjartan Poskitt's Fun Maths Videos
Mode: MANDV 143-146
Modulus (MOD function): PSAUS 98, CODES 148-149, The Modulus 105 Trick
Money: PSAUS 70-94, interest and e KEY 180-183, history AWAR 135-144
Moon: how fast does it move, siderial and synodic months EQEA 42-43
Multiplication: SOS 80-98, AWAR 93-101, Russian Peasant Multiplication EQEA 17
Music: MMoE 61-64, How many different tunes can you play on a piano? EQEA 7-12, Why do some musical notes sound awful together?, How do guitar strings make different notes?, The sounds of SIN and SQUARE waves
Mutually exclusive outcomes: LUCKY 106
Nanometer: DMEAS 47
Nets (of solids): ASAS 174-178, SAVSH 128-136 the 11 nets of a cube see: The Research Lab
Newton: PSAUS 64-65. For a lot more information on forces, see "Isaac Newton and His Apple" by Kjartan Poskitt 144-157
Nim games: MOM 118-123
Noughts and crosses: 4-dimensional MMoE 53, 3D noughts and crosses
Numbers: KEY, The link between Squared Triangle and Cube Numbers
Number facts: The Most Pathetic Facts in Maths
Number tricks: MOM 133-156, The 7-11-13 trick, The Impossible Guess, The Missing Digit Trick, Riverboat Lil's Mindreader trick
Octahedron: PSAUS 149, SAVSH 121. 125, 127, 133-134
Odd and Even numbers: AWAR 15-16
Odds: LUCKY 38-39, 153-161
Origami: ASAS 155-162
Palindrome numbers: MM2 107-108
Parabola: x2 graphs PHX 139- 144
Paradox: BBB 25-28
Parallax: FANG 150, 153
Parallelogram: PSAUS 134
Parallel lines: how to draw FANG 18
Parsecs: FANG 155-158
Pascal's Triangle: MMoE 72-80, for coefficients of (a+b)n PHX 100, probability LUCKY 61-77, combinations LUCKY 96-99, Pascal's Triangle How to get Fibonacci series see THE RESEARCH LAB
Pendulums: PSAUS 68
Penrose Roger: tiles SAVSH 90-91, The Penrose Chickens and Tiles
Pentagon: how to fold from paper SAVSH 97-98
Pentagonal Number: PSAUS 19
Pentominoes: MM2 16-20
Percentages: SOS 171-178, PSAUS 72, MANDV 112-117
Perfect Numbers: KEY 136-146
Perimeter: ASAS 118-128, PSAUS 12, 116, MM2 99-106, EQEA 75-77
Permutations: PSAUS 103-105, LUCKY 81-88, DBB 46-47
Perpendicular bisector: ASAS 32,95 SAVSH 22-26
PI: ASAS 52-57, KEY 174-178, PSAUS 15, 150-152, LUCKY 143-147, MM2 89-94, EQEA 24
Picometer: DMEAS 47
Pizza cutting: PSAUS 31, Chopping Pizzas
Planets: distance from sun MMoE 90
Plato: ASAS 167-170
Poker hands (chances of): MMoE 84, Chances of different hands of playing cards
Polygons: ASAS 129-154, SAVSH 56-99, PSAUS 116-126, tan area formula FANG 126-128, The Research Lab
Powers: BBB 117-121, AWAR 168-169, MM1 15-18
Prime factors: MANDV 43-48
PRIME NUMBERS: explanation MANDV 40-44, SOS 133-137, KEY 90-112, MMoE 12-17, MM1 46-51, Sudoku prime SUD 126, The SUDOKU Prime, use in codes CODES 148-149, The Prime Numbers Trick, The Prime Counter Mersenne Primes KEY 100, 142 The Research Lab Sieve of Eratosthenes MMoE 14, Sieve of Eratosthenes, How to write a Massive Prime Number!
Prince Rupert's Cube: EQEA 82
Profit: PSAUS 70-74
Proportion: FANG 30-31
Protractor: DMEAS 120-121, FANG 16-17
Pursuit curves: MMoE 44
Puzzles: DBB whole book, SUD, KAK, Puzzle Page, Dreaded Kjarposkos, Murderous Brainbending Puzzles also see "Sam Loyd" below
Pyramid: PSAUS 10, 146 What is the volume of a pyramid? With proof.
Pythagoras: MMoE 19-22, MM2 81-88 construction theorem proof SAVSH 148-159, EQEA 25-28, cut and paste theorem proof EQEA 26, ASAS 202-207 How do guitar strings make different notes?
Quadratics: solving equations and formula PHX 53-66, PSAUS 138, Solving Quadratics by Completing the Square, Quadratic calculator
Queens: The Eight Queens Chess Puzzle
Radians: DMEAS 124
Ramsey Theorem: EQEA 127-129
Ratios: FANG 30-37, trigonometry FANG 59
Rectangle: formulas PSAUS 10-13 How to turn a Rectangle into a Square of the same area
Reducing fractions: MANDV 49-51
Regions: Surprising Regions Formula
Regular Solids: SAVSH 121-136, formulas for surface area and volume PSAUS 149,
Regular Solids - formulas for volumes
Research Lab: THE RESEARCH LAB
(With answers to a very wide variety of odd maths questions!)
Rhombus: PSAUS 135
Richter Scale: Earthquake measurements
Right angle: MM1 72
Right angled triangles: MM2 81-88
Roman numerals: MM1 27-31
Rough sums: SOS 198-206
Rounding off: AWAR 145-152, MM1 126-129
RSA codes: CODES 145-157
Rubik's Cube: EQEA 83
Russian Peasant Multiplication: EQEA 17
Sam Loyd: The Sam Loyd Sliding Block Puzzle, Sam Loyd's Get Off The Earth Puzzle, Sam Loyd's Eight Queens Puzzle
Sampling: LUCKY 149-152
Scale: FANG 20-29
Scoville rating: Hotness of chilli pepper measurement
Scrambled Message Code: Scrambled Messages
Sector: PSAUS 156
Segment: PSAUS 157
Semicircle: right angle SAVSH 12-13,
Semiperimeter: PSAUS 116
Set Square: FANG 17-18
Shadow Stick: DMEAS 66
Sierpinski's Triangle: MMoE 80
Sieve of Eratosthenes: MMoE 14, Sieve of Eratosthenes
Significant digits/figures: AWAR 145
Simulaneous Equations: graph solving PHX 136-137, elimination and substitution PHX 147-156
Sin: FANG 60-66, 60º, 0º, 90º, 45º FANG 88-92, getting values by drawing FANG 94-96, sin formula PSAUS 120, sin formula FANG 114-118, triangle area formula FANG 128-130
Sine wave: FANG 165-174, The sounds of SIN and SQUARE waves
Skewes' number: EQEA 125
Sohcahtoa: FANG 71
Space: size of moons, planets, stars MMoE 88-93
SPEED: PSAUS 38-60, BBB 76-92, MM2 61-73
Sphere: PSAUS 10, 170-172 packing into a box EQEA 150-151
SQUARE (shape): how to draw with ruler and compasses SAVSH 74-76, how to fold SAVSH 94, dividing a square into smaller squares all of different sizes EQEA 29.
SQUARE (x2): KEY 43-56
Square Pyramid Numbers: KEY 63-64, PSAUS 20
Square Roots: EQEA 18-22, How to work out Square Roots without a calculator, square root of i The Research Lab
Stamps: formula for number of ways of tearing from a sheet PSAUS 21-24, 196-197,
Matthew Sheeran's Amazing Stamps Formula!
Standard Form: DMEAS 56-63, MM1 130-135
Star: distance away FANG 147-158, sizes of MMoE 93
Subtraction: SOS 35-54, AWAR 53-70
Sudoku: how many possible grids? SUD 122-127, The SUDOKU Prime
Symmetry: MM1 136-141
Tan: FANG 69-71, 45º FANG 94
Tangents: SAVSH 114
Teachers: Teacher Resource Page
Temperature: DMEAS 169
Tessalation: ASAS 150-154, SAVSH 88-91, MM1 19-21
Testing for factors: MANDV, KEY 108-111, Testing if numbers divide by 11, 7 or 13, The 11 Test
Tetrahedral Numbers: KEY 62-63, PSAUS 19, 90
Tetrahedron: PSAUS 148-149, SAVSH 121, 125, 127, 131, 133
Thales: BBB 21, SAVSH 12-13,
Think of a number tricks: MOM 39-47, PHX 79, A few tricks from The Magic Of Maths
Tic-tac-toe: 4-dimensional MMoE 53, 3D TTT puzzle
Time: DMEAS 158-167, see Speed, Acceleration, Pendulums
Times tables: SOS 55-80, AWAR 71-92
Kjartan Poskitt's Fun Maths Videos
Topology: MMoE 38-42, bridge crossing and drawing problems MM2 136-145 fluid handcuffs EQEA 142-143
Torus: PSAUS 173-174, volume The Research Lab
Trancindental numbers: KEY 174-183
Trapezium: PSAUS 139-142,
Calculating the Area of a Trapezium without the height!
TRIANGLES: ASAS 35-48, SAVSH 39-65, formulasPSAUS 126-134 constructing FANG 38-45, sin area formula FANG 128-130
Triangle Numbers: MM2 123-130, KEY 54-56, PSAUS 17-18, 21, 89, MMoE 18, The link between Squared Triangle and Cube Numbers, KEY 64-65
Triangulation: FANG 133-136
Tricks: DBB, PHX 74-90, Professor Fiendish's Tricks and Games
Trigonometry: FANG (whole book), PSAUS 121
Trisecting an angle: MMoE 30, How to Trisect an Angle
Unit fractions: PSAUS 192
Units of measurement: DMEAS 168-174, Some Unusual Units
Universe: size of EQEA 61
Vector: EQEA 69-72
VIDEOS: Kjartan Poskitt's Fun Maths Videos
Vigenere Code System: Vigenere Grids
Volume: measuring DMEAS 127-133
Vulgar Fractions: SOS 148-152
Wallpaper: Download your Murderous Maths Wallpaper for your computer desktop.
Waves: sin cos tan FANG 165-180
Weights: smallest number needed for balance scales EQEA 93-97
Y intercept (on graphs): PHX 135
Yahtzee: chances of throwing combinations MMoE 83
Zero: invention of 0 MM1 35-36, impossible proof PHX 157
Murderous Maths Main Index Page
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