Why do animals curl up when sleeping, and why do the bodies of sea creatures such as the octopus have little volume but a large surface area? It all comes down to maximising efficiency, which is a function of an object's surface area and volume.
You don't ignore an army Drill Sergeant when he yells, 'About, Face!' to nervous recruits. But how many times will he have to bark orders if not all recruits are asked to do what he says at the same time. This poses an interesting problem in mathematics which we will explore.
Basic shapes can be combined in different ways to produce different areas. Each shape is not altered in any way, so the challenge is to figure out why this is happening. These cater to the puzzle enthusiast as well as to the mathematician looking for formal proof.
We know that every non-zero real number raised to a power exists, but what happens if both the base and the power are zero? Is the answer 0, 1, or something else? We will examine this situation in some detail.
The theorem of Pythagoras is well known, showing the relationship between the areas of squares on the sides of right-angled triangles. However, it may not be realised that the theorem can also be used to show relationships between shapes other than squares.
Few people would have predicted the mathematical controversy that would follow the first time the 'three door problem' was played on the quiz show, Let's Make A Deal. The game is easy to play, but the implications in terms of probability theory were controversial and divisive.
An enthusiastic teacher goes overboard to discuss the famous Pancake Problem, bringing in sorting algorithms and recursion techniques in an analysis of stacks of different sized pancakes. Intuitive conclusions are drawn regarding the number of pancake tosses a hapless chef needs to make.
The area of a flat shape can be estimated by dividing it into unit squares and counting their number. Pick's Theorem provides a method to find the exact area of a polygon drawn on a dotted grid. We look at how the Theorem works and establish a proof using Euler's formula.
Shaking hands is one of the most common activities we do. But have you considered just how many handshakes you would have to make in a room full of people? We will delve into the mathematics of handshaking and combinatorial analysis.
A casual summer job with a motley crew of tradesmen almost made me regret that I wasn't back at University. This was until I came to understand their special brand of humour, knowledge and their worship of Pythagoras.
Reminiscing can evoke both pleasant and painful memories. Share some of my boyhood adventures that took place at a simpler time and a simpler place.They focus on the local creek and dump site, but any location could have inspired the types of experiences when left to a boy's imagination.
Here are some resources that can be used at home to investigate some key areas of mathematics with your children. The explorations are open-ended.
Virtually every processed item, be it animal, vegetable or mineral, has associated with it a signature known as a barcode. This article examines two standard footprints that provide substantial information about a product; EAN-13 and ISBN.
There are many things parents can do to assist their child to cope with the rigors of mathematics. This article provides specific examples and general advice to parents who can act as mentors.
Why do you weigh less in an aeroplane than you do on land, and how does gravity play a part? The connection between mass, weight and gravitational acceleration can explain the best way to instantly reduce your weight.
A number of stories surround the puzzle known as Tower of Hanoi, Tower of Brahma and Lucas' Tower. Over the years, the puzzle has provided challenge to people in all walks of life, including mathematicians, computer programmers and strategists.
There are many mathematicians throughout history who have left their mark in mathematics. This is a tribute to some of them, presented in rhyme and focusing on each mathematician's principal contribution.
Is there a difference between incentive and motivation? Let's explore this with reference to some real-life examples we can all appreciate within a school setting.
Here is a dissection of a selection of mathematics words whose assumed definitions bears no resemblance to their actual meaning. No wonder people say maths is hard!
Ever tried to fold paper as many times as you could? It is widely accepted that you can't fold it more than 7 times. Let's investigate this popular (mis)conception.
The English language is universal, but it needs a revamp. With my tongue firmly in my cheek, I identify aspects that need to be overhauled. Let's dispense with the ceremony of correct grammar and jump straight into how much damage we can do with my recommendations.
Mathematics is replete with paradoxes. Let's look at two of them to fuel your desire to see whether or not this is true.
Eddy was naughty and planned things carefully, but even he did not predict what would happen to Prince, the frog.
The dreaded parent-teacher interview is looming, but are you ready?
As a parent, you try to help with homework. But how good are you in mathematics? Here are some simple maths questions to gauge your comprehension.
Riddles are fun and good exercise for the grey matter, but they can be frustrating. To solve most of the riddles contained in this article , you must not assume the obvious. See how you go with this baker's dozen.
Don't let mind readers and magicians mess with your mind with number tricks. Learn their secrets and beat them at their own game.
Do you ever wonder how Magic Squares are created? Well, stop worrying. I'll show you how to construct them using just a few easy to follow rules.
Have you heard of Fibonacci numbers? In this article, we explore the ubiquitous Fibonacci sequence and its presence in nature and in many aspects of our life.
The difference between recycling and hoarding is a subtle one. Take the test to see if your accumulation of treasures is a euphemism for trash and clutter.
The advertisements on the pages of comic books may seem innocuous, but they can lull a boy into real strife.
Have I gone too far in accommodating my desire to emulate the traditions of calmer times?
If teachers carried their jargon (verbal baggage) home with them, what would it be like?
Good grammar and mathematics are not irreconcilable. A class learns this lesson in a most unexpected way.
Can't stand maths but you have to pass the subject? Ensure you pass those dreaded tests by following these guidelines.
Parents, watch out for your kids. You don't know the mischief a boy with a healthy imagination can create.
A school inspector had ultimate authority, so when he planned a visit to a school, who should be more afraid, the teacher or the students?
Want a speedy entry and exit when you do your supermarket shopping? Then this guide is for you.
Teaching is for the young at heart and for the passionate. I found this out a long, long time ago. But as they say, regrets, I have a few.
Why do we insist in saying "Fish and Chips" rather than "Chips and Fish"? And why "in and out" in preference to "out and in"? Human conditioning is the key.
New teachers need guidance to learn the ropes of their profession. This primer will do anything but that.
It is said that no good deed goes unpunished, and this is certainly true for poor Sarah during her day at the beach.
A teacher is blessed if he has students willing to learn, but is this always the case?
In school, we all get into strife occasionally, but it hurts more when you know you are innocent.
We are all blessed (or cursed) with what our parents bequeath us, including a name.
If you have played the 'laughing clown' game at the carnival, you appreciate how frustrating it is that a prize is always just out of your reach. Now let's mathematically explore why this is the case.
When you can't do something, you may as well admit it and move on. This applies especially to new schoolteachers.
Do you know the origin of the game of chess? We take a look at one version of its history and continue to a version of solitaire involving the knight.
A teacher must be diligent and thoughtful when assigning passwords to students ready to rebel.
To make the connection between probability and the value of pi can be onerous.
A teacher's quest to enlighten math students can take unexpected turns. Let's see how one teacher livens up the lesson by involving the class in a quiz game show
Can we escape the shackles of obsessive compulsive behaviour manifested in our daily routine?
We all experience the first stirrings of "love" in school, but how can we act on it without enveloping oneself in the blanket of humiliation?
"Are you a bad driver, Dad?" Sally asked me one evening as we watched TV footage of a car that had landed in someone's swimming pool. "Not on your life!" I instantly replied. "I've only had a dozen or so accidents in 30 years of driving, and none...
It was one of those hot summer days, just before lunch. The air-conditioning was running a poor second to the humidity and windows were flung open in anticipation of the predicted cool change. Students languidly copied from the board whilst I...
What is mathematics? Responses will vary. "Numbers," someone will say, others may reply with, "Doing things with numbers and letters and other symbols," whilst pragmatists will contend that "Mathematics is a necessary tool for day to day living." ...
A teacher's portfolio is replete with lesson plans which promise nirvana and deliver purgatory. Semester examinations were over, reports were written and holidays were teasingly around the corner. There was a disquieting sense of calmness permeating...
A teacher does not have the luxury of having a bad day, especially when they should be on their best behaviour. Nowhere is this truer than when my school opened their doors one evening to showcase all that is good and proper. Was the day really...
It is never easy for a teacher to teach mathematics. Students instinctively recoil in fear, disgust or apathy at the mere mention of the subject. Indeed, anyone foolhardy enough to mention to their friends that math is not that bad -that in fact,...
I was seated facing the class, animating arms and legs not unlike a talking version of Marcel Marceau. "I'm driving to school," I said, making "vroom vroom" sounds that were better suited for a kindergarten playgroup. "Ahead of me are traffic...
Stealing Chopsticks Is Wrong Tom was passionately explaining some aspect of psychology. "Ultimately, our behaviour as teachers is a self-fulfilling prophecy. A classic study of Maslow's Hierarchy Of Needs." "Huh?" I teased. Tom teaches psychology...
Gone are the days when you would walk into a bank to hear a friendly human ask you, "How much do you wish to withdraw today, Mr Jenkins?" and be farewelled with a gift of a money box. Blessed were the days when you did not have to have a doctorate...
So You Want To Do It Yourself? "It's so simple, a child can do it!" How many times have you come across this pervasive statement, a key element of false advertisements that extol the economic advantages and gratification afforded by "assemble it...
Dear Dr Freud, I suffer from a condition that is becoming increasingly common. It is what I refer to as queuephobia, a desire to fantasize when confronted by any situation involving a queue of people. I am providing you with a description of...