Mathematics Masterclasses for Young People

ISBN : 9780198801214

Michael Sewell
128 ページ
156 x 234 mm

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.


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


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 inspired the 1997 OUP edited work Mathematics Masterclasses - Stretching the Imagination, and led to this current book.