Year 1998 - Volume 34
2020 - Present

Peter Hilton and Jean Pedersen
Those of you who have taken plane geometry will know that the Greeks were fascinated with the challenge of constructing regular polygons - that is, those polygons with all sides of the same length and all angles equal.

S. M. Stewart
In an interesting problem, which as my title suggests also has interesting historical roots, physical insight can often simplify an otherwise complicated mathematical problem.

Peter G. Brown
If you were to ask a variety of people what  was, you would probably get a variety of different answers.

Q1015. Quantities of coins are available denominated at one tenth, one twelveth and one sixteenth of a penny. How can these be used to settle a debt of one two hundred and fortieth of a penny? The giving of change is allowed.

Q1015. Quantities of coins are available denominated at one tenth, one twelveth and one sixteenth of a penny. How can these be used to settle a debt of one two hundred and fortieth of a penny? The giving of change is allowed.

Peter Hilton and Jean Pedersen
Experiment 1: Figure 1(a) shows a portion of tape which has been folded using the D1U1 -procedure, with the first few (say 10) triangles cut away.

Peter Hilton and Jean Pedersen
In Part 1 (Parabola Vol. 34, No 1) we introduced you to a basic construction whereby we folded down m times at the top of a tape and folded up n times at the bottom of the tape (see Figure 1).

Michael J. Nealon
Semi-definite optimization is a very new topic in the branch of applied mathematics known as optimization. Optimization refers to the process of finding the best way of achieving a goal.

Let x,y and z be integers. Prove that if 2x+4y+5z is a multiple of 17 , then so is 3x+6y−z .

Q.1025 Find the smallest number that when divided by 29 leaves the remainder 23 and that when divided by 37 leaves the remainder 31 .

Q.1015 Quantities of coins are available denominated at one tenth, one twelveth and one sixteenth of a penny. How can these be used to settle a debt of one two hundred and fortieth of a penny? The giving of change is allowed. .

Peter Hilton and Jean Pedersen
In our paper we showed how to fold a regular 7 -gon - and much else besides! We showed which convex polygons could be folded by a period-2 folding procedure these turned out to be those polygons whose number of sides, s , had the form
s=(2m+n−1)/(2n−1)

Bruce Henry and Simon Watt
One of the most famous problems in the history of dynamics is the brachistochrone problem.

SENIOR DIVISION, Equal first prize of \$200 and a certificate: VARODAYAN David, Sydney Grammar School; ELLIOT Justin Koonin, Sydney Grammar School

Q.1035 Find all positive integers n and m such that n is a factor of 4m−1 and m is a factor of 4n−1 .

Q. 1016 Show how six cylindrical pencils of equal radius each with neither end sharpened can be put into mutual contact along their curved surfaces.