# 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?, 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

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

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, 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

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: 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

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 Jokes Page

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, 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, 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 (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

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

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

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