π in the Sky is a semi-annual publication of students, parents or anybody interested in math education (be sure to include your full name and phone number). Cover Page: In October 2001, π in the Sky was invited by the principal of Edmonton’s Tempo School, Dr. Kapoor, to meet with students in grades 10 and 11. The picture on the cover page was taken by Henry Van Roessel at Tempo School PIMS is supported by the Natural Sciences and Engineer- during our visit. More photos from that visit are published on ing Research Council of Canada, the British Columbia page 28. Information, Science and Technology Agency, the Al- If you would like to see your school on the cover page of π in the berta Ministry of Innovation and Science, Simon Fraser Sky, please invite us for a short visit to meet your students and staff. University, the University of Alberta, the University of British Columbia, the University of Calgary, the Univer- sity of Victoria, the University of Washington, the Uni- CONTENTS: versity of Northern British Columbia, and the University The Language of Mathematics of Lethbridge. Timothy Taylor ...................................3 This journal is devoted to cultivating mathematical rea- soning and problem-solving skills and preparing students Tic-Tetris-Toe to face the challenges of the high-technology era. Andy Liu, University of Alberta .......................4 Editors in Chief Nassif Ghoussoub (University of British Columbia) Weierstraß Tel: (604) 822–3922, E-mail: [email protected] Volker Runde, University of Alberta ....................7 Wieslaw Krawcewicz (University of Alberta) Tel: (780) 492–7165, E-mail: [email protected] Life and Travel in 4D Associate Editors Tomasz Kaczynski, Universit´ede Sherbrooke .............10 John Bowman (University of Alberta) Tel: (780) 492–0532 E-mail: [email protected] Shark Attacks and the Poisson Approximation Dragos Hrimiuc (University of Alberta) Tel: (780) 492–3532 E-mail: [email protected] Byron Schmuland, University of Alberta ................12 Volker Runde (University of Alberta) Tel: (780) 492–3526 E-mail: [email protected] The Rose and the Nautilus Editorial Board A Geometric Mystery Story Peter Borwein (Simon Fraser University) Tel: (640) 291–4376, E-mail: [email protected] Klaus Hoechsmann, University of British Columbia ........15 Florin Diacu (University of Victoria) Tel: (250) 721–6330, E-mail: [email protected] Three Easy Tricks Klaus Hoechsmann (University of British Columbia) Ted Lewis, University of Alberta Tel: (604) 822–5458, E-mail: [email protected] .....................18 Michael Lamoureux (University of Calgary) Tel: (403) 220–3951, E-mail: [email protected] Inequalities for Convex Functions (Part I) Ted Lewis (University of Alberta) Dragos Hrimiuc, University of Alberta .................20 Tel: (780) 492–3815, E-mail: [email protected] Copy Editor Math Challenges ............................26 Barb Krahn & Associates (11623 78 Ave, Edmonton AB) Tel: (780) 430–1220, E-mail: [email protected] Math Links ..................................27 Addresses: Our School Visit π in the Sky π in the Sky Don Stanley, University of Alberta .....................28 Pacific Institute for Pacific Institute for the Mathematical Sciences the Mathematical Sciences 449 Central Academic Blg 1933 West Mall University of Alberta University of British Columbia Edmonton, Alberta Vancouver, B.C. T6G 2G1, Canada V6T 1Z2, Canada Tel: (780) 492–4308 Tel: (604) 822-3922 Fax: (780) 492–1361 Fax: (604) 822-0883 E-mail: [email protected] http://www.pims.math.ca/pi Contributions Welcome π in the Sky accepts materials on any subject related to mathematics or its applications, including articles, problems, cartoons, statements, jokes, etc. Copyright of material submit- ted to the publisher and accepted for publication remains with the author, with the understanding that the publisher may re- produce it without royalty in print, electronic and other forms. Submissions are subject to editorial revision. We also welcome Letters to the Editor from teachers, c Copyright 2001 Sidney Harris 2.