# A-Z Index

0.99999... : 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?

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?

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

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

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

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)

Cone: *volume of cone, area of sloping side* PSAUS 172 What is the volume of a cone?

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: PSAUS 172

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 (x^{3}): KEY 57-60, curve on graphs PHX 142

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

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

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

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

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* 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 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

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, The Football Team Illusion, Lil's Missing Card Illusion, Sam Loyd's Get Off The Earth Puzzle, Akiyoshi Kitaoka's Distorted Squares, Three Magical Colour Illusions!,
The Chess Board Illusion

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

Kaprekar: KEY 115

Kepler: PSAUS 62

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

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

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: x^{2} 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

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, 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

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 (x^{2}): 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

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

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

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, *formulas*PSAUS 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

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