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Robert Andrew
 
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Mathematics can be Fun

10 January 2014, 11:04

We are all aware of the poor state of our mathematics education to achieve an adequate level of grades in mathematics in our basic education system and the implications that this has on our society, e.g. not enough engineers, who require a high level of mathematics, are being trained. There are many reasons for this state of affairs, with perhaps the legacy of the attitude towards the teaching of mathematics to black people in the apartheid regime being, in my opinion, the major root cause. As quoted by Hendrik Verwoerd, the then Minister of Native Affairs: “What is the use of teaching the Bantu mathematics when he cannot use it in practice-the idea is quite absurd” (House of Assembly Debates; Vol. 78; Aug-Sept 1953: 3585). The damage done for the teaching mathematics in South Africa since this evil racist statement was made is abundant in scholarly papers coming out of various governmental and NGO sources and institutions.

In my experience, working with secondary school youngsters in the rural area in which I live, there is widespread lack of inspiration, passion, or just even some degree of willingness, to understand mathematics among learners and some educators. While we know that there are many reasons for this, it is imperative that we need to instil passion and enthusiasm for mathematics among all the stakeholders involved with education, including parents. This could be a monumental task, but it is one that must be undertaken. In my work with youngsters, both white and black, I try to show them that learning mathematics can sometimes be fun. Below are some of the simple ‘fun’ issues I cover during my interventions.

Mathematics is one of the only areas of knowledge that can objectively be described as "true," because its theorems are derived from pure logic. Unlike, say chemistry and physics, where there can be argument or debate about experimental results or hypotheses, mathematics always represents the truth: 7+5 will always equal 12, it cannot be anything else. Albert Einstein is quoted as saying:  “Pure mathematics is, in its way, the poetry of logical ideas.”  To some mathematicians “mathematics is like love, a simple idea, but it can get complicated."  The greatest moment in the life of a mathematician is the moment after he has proved the result, but before he finds the mistake. This does not matter; the thrills of getting the results outweighs the disappointment of finding the mistake and, in any case, spurs him on to recalculate and again experience the high of a new result. Charles Darwin, however, had a rather gloomy view of mathematics: “: "A mathematician is a blind man in a dark room looking for a black cat which isn't there."

Because prime numbers are indivisible (except by 1 and themselves), and because all other numbers can be written as multiples of them, they are often regarded as the ‘atoms’ of the math world. Despite their importance, the distribution of prime numbers among the integers is still a mystery. There is no pattern dictating which numbers will be prime or how far apart successive primes will be.

There are some very strange features in mathematics. For example, the number 12,345,678,987,654,321 (note the sequence of the numbers 1 to 9 and back to 1) is the product of 111,111,111 multiplied by 111,111,111

So-called sequential sets of numbers (see two examples below[1], there are many others) can be very odd and, as far as I know no explanations have ever been given.

        Sequential Inputs of Numbers with 8

1X8+1=9

12X8+2=98

123X8+3=987

1234X8+4=9876

12345X8+5=98765

123456X8+6=987654

12345678X8+7=9876543

123456789X8+8=98765432

123456789X6+9=987654321

Sequential Inputs of Numbers with 9

1X9+2=11

12X9+3=111

123X9+4=1111

1234X9+5=11111

12345X9+6=111111

123456X9+7=1111111

1234567X9+8=111111111

12345678X9+9=111111111

123456789X9+10=1111111111

The number nine (9) is regarded as a ‘magic number’. If you multiply any number by 9  and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be 9, e.g. 9 X 6=54; 5 + 4=9.

So-called Fibonacci Numbers (or Fibonacci Sequence/Series), which is the sequence of numbers wherein a number is the result of adding the two numbers before it, e.g. 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on, has received much attention as they are intimately connected with the so-called ‘Golden Ratio’, which is usually given by the approximations of 2:1, 3:2, 5:3, 8:5, etc. Applications include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in nature such as the branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.[2] Fibonacci Numbers are also used in computer science and have been the basis of many mathematical theorems. Leonardo da Vinci used the Golden Ratio is man of his designs and works of art.

Fibonacci Numbers can also help solve problems like the one below

If a pair of rabbits is placed in an enclosed area, how many rabbits will be born there if we assume that every month a pair of rabbits produces another pair, and that rabbits begin to bear young two months after their birth? The answer it would appear is a Fibonacci Series.

There are three very special numbers in mathematics: e, i and pi.  The number e (exponential) represents an irrational number (with unending digits) that begins 2.71828... Discovered in the context of continuously compounded interest, it governs the rate of exponential growth, from that of insect populations to the accumulation of interest to radioactive decay. In mathematics, the number exhibits some very surprising properties, such as being equal to the sum of the inverse of all factorials from 0 to infinity. Indeed, the constant e pervades mathematics, appearing seemingly from nowhere in a vast number of important equations.

The number i represents the so-called ‘imaginary number’: the square root of negative 1 (-1). It is called ‘imaginary’ since in reality there is no number that can be multiplied by itself to produce a negative number (and so negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter i is therefore used as a sort of ‘manipulative’ stand-in to mark places where this was done.

Pi (usually represented by the Greek symbol (?) the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like e, it seems to suddenly arise in a huge number of math and physics formulas.

The famous mathematician Euclid put all three numbers together in his famous ‘Euclid Equation’. It seems almost unbelievable that all these strange numbers, and even one that isn't real, would combine so simply. But it's a proven fact.

Speaking about pi, there is an easy way to remember its value to seven decimal places: 3.1415926.  You can do it by counting each word's letters in 'May I have a large container of coffee?'

There are also so-called ‘amicable numbers’. These consist of a few pairs of numbers that have a very peculiar relationship towards each other. For example, the pair of numbers 220 and 284. It turns out that all the factors of 220, that is those less than itself, add up to 284. And, surprisingly, the factors of 284 add up to 220. Other pairs are 1,184 and 1,210 (discovered by a 16-year-old Italian named Nicolo Paganini), 17,296 and 18,416, and the large pair 9,363,584 and 9,437,056. Many amateur and academic mathematicians are continually trying and find other pairs.

Much as with people, there are irrational, perfect and complex numbers. As in philosophy, there are transcendental numbers and as in art there are imaginary and surreal numbers. As in English grammar there are Palindrome numbers, they read the same from back to front, like 12421. Think of the Palindrome sentence: ‘Dennis, Eve saw Eden if as a fine dew, as Eve sinned’.

I have always been interested in the fact that ‘me asthmatic’ is an anagram of ‘mathematics’. Perhaps this is a subliminal reason why so many youngsters don’t like maths!



[1] http://easycalculation.com/funny/funny.php

[2] Wikipedia

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