This work consists of a series of "masterclasses", short sessions of mathematics beyond the standard school syllabus aimed at 10 to 15-year-olds with a flair for mathematics who want to stretch themselves.
This work consists of a series of "masterclasses", short sessions of mathematics beyond the standard school syllabus aimed at 10 to 15-year-olds with a flair for mathematics who want to stretch themselves.
Michael Sewell is Emeritus Professor of Applied Mathematics at the University of Reading. He has B.Sc., Ph.D, and D.Sc. degrees from Nottingham University and is a Fellow of the Institute of Mathematics and its Applications, and of the Royal Meteorological Society. During the decade starting in 2001, he devised and delivered weekly "Mathematics Masterclasses" to selected groups of able ten-year-olds at Bisham School near Maidenhead, which followed on from the 1997 OUP edited work "Mathematics Masterclasses - Stretching the Imagination", and led to this current book.
Inhaltsangabe
1: Introduction 2: Spin-up 3: Subject definitions 4: Odds and evens 5: Solving equations 6: Weighing the baby by algebra 7: Prime numbers 8: Don't jump to conclusions 9: Euler's formula 10: Goldbach's guess 11: Perfect numbers 12: Euclid's theorem 13: Mathematical symbols 14: Medicine problem 15: Dramatic dates 16: The foggy day problem 17: Angles 18: Angles inside a triangle 19: Angles inside a quadrilateral 20: Angles inside a polygon with n sides 21: Method for nding the centre of a circle 22: Angles in a sector of a circle 23: Orthocentre 24: Arithmetic progression 25: Leavers from an expanding school 26: Isaac Newton 27: Geometric progression 28: Zeno's paradox 29: Big birthday problem 30: Sundays in February 31: Think of a number 32: Hand shaking 33: Losing money to the bank 34: Supermarket oers: deal, or no deal? 35: Imperial and metric 36: House prices in Maidenhead 37: Fahrenheit and centigrade 38: Small things 39: Leonardslee cake 40: Halving areas 41: Isosceles tiling 42: Roman numerals 43: New money for old 44: Distance measures 45: Weight measures 46: Perimeter-diameter ratios 47: Fibonacci numbers 48: Quadratic equations and the Fibonacci sequence 49: Pascal's triangle and the Fibonacci sequence 50: Golden ratio 51: Pythagoras and the Fleet Air Arm 52: Fermat's Last Theorem 53: Another proof of Pythagoras' Theorem 54: A third proof of Pythagoras' Theorem 55: Another application of Pythagoras' Theorem 56: Pythagorean triples 57: Nautical notation 58: Paper sizes 59: Paper sizes and an innite sequence of triangles 60: Magic squares 61: Binomial squares 62: Some special squares 63: The nine-point circle 64: The thirteen-point circle 65: Cardioid 66: Irregular hexagons and Pappus' theorem 67: Regular hexagons 68: The rugby riddle 69: Family trees in people and bees 70: The tethered goat problem 71: Fencing the bulls 72: Surprises 73: Sewell's spirals 74: Prime diagonals 75: Cubic cusp in the classroom 76: Nature's circles 77: Rainbow 78: Basis and bases of arithmetic 79: Lunes 80: An octet of equal circles 81: Alternative construction of the octet 82: Triangle constructions 83: A mosaic of equal circles 84: Intersection of equal spheres 85: Christmas cracker 86: Ostrich egg 87: Holditch's Theorem 88: A coee shop problem 89: Step waves 90: References 91: Author information
1: Introduction 2: Spin-up 3: Subject definitions 4: Odds and evens 5: Solving equations 6: Weighing the baby by algebra 7: Prime numbers 8: Don't jump to conclusions 9: Euler's formula 10: Goldbach's guess 11: Perfect numbers 12: Euclid's theorem 13: Mathematical symbols 14: Medicine problem 15: Dramatic dates 16: The foggy day problem 17: Angles 18: Angles inside a triangle 19: Angles inside a quadrilateral 20: Angles inside a polygon with n sides 21: Method for nding the centre of a circle 22: Angles in a sector of a circle 23: Orthocentre 24: Arithmetic progression 25: Leavers from an expanding school 26: Isaac Newton 27: Geometric progression 28: Zeno's paradox 29: Big birthday problem 30: Sundays in February 31: Think of a number 32: Hand shaking 33: Losing money to the bank 34: Supermarket oers: deal, or no deal? 35: Imperial and metric 36: House prices in Maidenhead 37: Fahrenheit and centigrade 38: Small things 39: Leonardslee cake 40: Halving areas 41: Isosceles tiling 42: Roman numerals 43: New money for old 44: Distance measures 45: Weight measures 46: Perimeter-diameter ratios 47: Fibonacci numbers 48: Quadratic equations and the Fibonacci sequence 49: Pascal's triangle and the Fibonacci sequence 50: Golden ratio 51: Pythagoras and the Fleet Air Arm 52: Fermat's Last Theorem 53: Another proof of Pythagoras' Theorem 54: A third proof of Pythagoras' Theorem 55: Another application of Pythagoras' Theorem 56: Pythagorean triples 57: Nautical notation 58: Paper sizes 59: Paper sizes and an innite sequence of triangles 60: Magic squares 61: Binomial squares 62: Some special squares 63: The nine-point circle 64: The thirteen-point circle 65: Cardioid 66: Irregular hexagons and Pappus' theorem 67: Regular hexagons 68: The rugby riddle 69: Family trees in people and bees 70: The tethered goat problem 71: Fencing the bulls 72: Surprises 73: Sewell's spirals 74: Prime diagonals 75: Cubic cusp in the classroom 76: Nature's circles 77: Rainbow 78: Basis and bases of arithmetic 79: Lunes 80: An octet of equal circles 81: Alternative construction of the octet 82: Triangle constructions 83: A mosaic of equal circles 84: Intersection of equal spheres 85: Christmas cracker 86: Ostrich egg 87: Holditch's Theorem 88: A coee shop problem 89: Step waves 90: References 91: Author information
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