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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.

The book is aimed to provide teachers with a source of novel and interesting topics to supplement their standard material, and as independent reading for pupils themselves.

It will be helpful to teachers who require interesting and novel topics, beyond the standard syllabus and normal textbook material, for capable pupils.

Cover:

Paperback

Edition Number:

1

ISBN:

9780198801214

Pages:

144

Author:

Sewell Michael

Publisher:

OXFORD UNIVERSITY PRESS

Release Year:

2017

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.

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