APPLIED PROBABILITY TRUST

Mathematical Spectrum

Editor: D. W. Sharpe (The University of Sheffield)

Mathematical Spectrum is a magazine for students and teachers of mathematics in universities, colleges and schools worldwide. It may be read by anybody interested in mathematics as a recreation. Mathematical Spectrum publishes articles from all branches of mathematics, as well as regular features on mathematics in the classroom, a computer column, letters, problems and solutions, book and software reviews. We welcome original student contributions and award annual prizes for the best ones published.

Forthcoming articles

Contents of recent issues

From the Editor (Volume 37, Number 3)
From the Editor (Volume 38, Number 1)
From the Editor (Volume 38, Number 2)
From the Editor (Volume 38, Number 3)
From the Editor (Volume 39, Number 1)
From the Editor (Volume 39, Number 2)
From the Editor (Volume 39, Number 3)
From the Editor (Volume 40, Number 1)
From the Editor (Volume 40, Number 2)
From the Editor (Volume 40, Number 3)

Sample problems

40.10 Let n > 7 be an integer such that n - 1 and n + 1 are both prime. Show that n²(n² - 4)(n² - 9) is divisible by 2721600.

(Submitted by Roger Cook, Pembroke, UK)

A solution will be published in Volume 41, Number 2.

40.5 Let P₁P₂P₃P₄P₅ be a regular pentagon, centre O, and let P be any point in the plane of the pentagon. For i = 1, 2, 3, 4, 5, denote by C_i the circle with centre P_i which passes through P, and denote the point of intersection of circles C_i and C_i+1 other than P by A_i (C₆ = C₁). Prove that the centre of gravity of A₁, A₂, A₃, A₄, A₅ is O.

Let A_i' be the foot of the perpendicular from P to P_iP_i+1 (P₆ = P₁). Show that A_i' is the midpoint of A_iP and that the centre of gravity of A₁', A₂', A₃', A₄', A₅' is the midpoint of OP.

(Submitted by Daniel Schultz (aged 13), Southbank International School, Hampstead, London, UK)

A solution will be published in Volume 41, Number 1.

Access details

All submissions should be sent to:

The Editor, Mathematical Spectrum                                 School of Mathematics and Statistics                                 The University of Sheffield                                       Sheffield S3 7RH, UK.
Email: spectrum@sheffield.ac.uk

MS ISSN 0025-5653 three times a year

Special Publication: A Mathematical Spectrum Miscellany
Have you got your copy of A Mathematical Spectrum Miscellany?
Published February 2000 by The Applied Probability Trust. Pp. vi + 198 (ISBN 0-902016-05-9).
This special celebratory publication brings together, in handy book form, reader's favourites from all areas of mathematics. Enjoy this varied selection of articles chosen from over 30 years of Mathematical Spectrum.
Prices are:
£12.00   or   US$23.00   or   A$30.00
For further information, contact Sue Boyles
(email: s.c.boyles@sheffield.ac.uk).

Subscriptions

One volume of Mathematical Spectrum is published in each British academic year.  Please note orders must be placed for complete volumes, beginning in September, and not for calendar years.  Each volume consists of three issues, published in September, January and May.

We accept orders at reduced prices for up to three years ahead.

Volumes 40, 41 and 42
(September 2007 to August 2010)
£35.40    or    US$72.00    or    A$87.60

Volumes 40 and 41
(September 2007 to August 2009)
£24.00    or    US$50.00    or    A$62.00

Volume 40
(September 2007 to August 2008)
£13.00    or    US$26.00    or    A$32.50

Back issues (price per volume)

Volumes 1-6       (2 issues per volume)   £5.50
Volumes 7-22     (3 issues per volume)   £7.50
Volumes 23-26   (4 issues per volume)   £9.50
Volumes 27-37   (3 issues per volume)   £10.00
Volume 38          (3 issues per volume)   £12.50
Volume 39          (3 issues per volume)   £13.00

For further information, contact Sue Boyles:
(email s.c.boyles@sheffield.ac.uk)
Telephone: +44 114 222 3922.
Fax: +44 114 272 9782

For information on any of the APT's publications, contact the Executive Editor:
Linda Nash
Applied Probability
School of Mathematics and Statistics
The University of Sheffield
Sheffield S3 7RH
UK
Telephone: +44 114 222 3920
Fax: +44 114 272 9782
Email: l.nash@sheffield.ac.uk