Magical MathsPresented By:

BenSianHolly

Martin

The nature behind Maths

It is believed that Ancient Egyptians used complex mathematics such as algebra, arithmetic and geometry as far back as 3000 BC, such as equations to approximate the area of circles.

• Babylonians measured the circumference of a circle as approximately 3 times the diameter, which is fairly close to today’s measurement which uses the value of Pi (around 3.14).

• Chinese mathematics developed around the 11th century BC and included important concepts related to negative numbers, decimals, algebra and geometry.

• Greek mathematics developed from around the 7th century BC, producing many important theories thanks to great mathematicians such as Pythagoras, Euclid and Archimedes.

• The symbols used for addition (+) and subtraction (-) have been around for thousands of years but it wasn't until the 16th century that most mathematical symbols were invented. Before this time math equations were written in words, making it very time consuming.

• The equals sign (=) was invented in 1557 by a Welsh mathematician named Robert Recorde.

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What special things are there about maths...

Armstrong NumbersArmstrong numbers involve squared numbers.

E.g. 153 = 13 + 53 + 33

Some other Armstrong numbers are:370, 371, 407

Strange things about the number: 666

The number 6 can be used in many ways...

666 = 63 + 63 + 63 +6 + 6 + 6

666 = 22 + 32 + 52 + 72 + 112 + 132 + 172

Vampire NumbersThe number 1260 is a vampire

number...

With 21 and 60 as fangs

Since that 21 x 60 = 2160

Others are: 1395 = 15 x 931435 = 41 x 531530 = 51 x 30

Numeric Palindrome with number 1

1 x 1 = 111 x 11 = 121

111 x 111 =123211111 x 1111 = 1234321

11111 x 11111 = 123454321111111 x 111111 = 12345654321

1111111 x 1111111 = 123456765432111111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Sequential Inputs of 9

9 x 9 = 8199 x 99 = 9801

999 x 999 = 9980019999 x 9999 = 99980001

99999 x 99999 = 9999800001999999 x 999999 = 9999980000001

9999999 x 9999999 = 99999980000000199999999 x 99999999 = 9999999000000001

999999999 x 999999999 = 999999990000000001

A Maths Trick...Think of a Number between 1 and 10...

Double your number...Add 6 to your result...

Half your answer (divide by 2)...Then finally take away your original

number...

Your answer is...

3

The ’11’ RuleEver wanted to times a two digit number by 11 easily?

E.g. 54 x 11 = ? Notice the hole

between the 2

numbers...(5_4)

Separate the 2 digits... (5_4)

Add the 5 and the 4 together...

Put the result (9) in the middle of the hole = 5 9 4.54 x 11 = 594

However, this rule will will only work with numbers that

are as big as 9.

The Magic of 9Table Sum of the digits of each product

1 x 9 = 9 0 + 9 = 92 x 9 = 18 1 + 8 = 93 x 9 = 27 2 + 7 = 94 x 9 = 36 3 + 6 = 95 x 9 = 45 4 + 5 = 96 x 9 = 54 5 + 4 = 97 x 9 = 63 6 + 3 = 98 x 9 = 72 7 + 2 = 99 x 9 = 81 8 + 1 = 9

10 x 9 = 90 9 + 0 = 9

The Magic of

9

Choose any two digit numbers and for each one reverse the digits and subtract the smaller number from the larger number Sum of the

Digits:

92 29 (92 - 29) = 63 9 x 7 6 + 3 = 9

14 41 (41 - 14) = 27 9 x 3 2 + 7 = 9

83 38 (83 - 38) = 45 9 x 5 4 + 5 = 9

17 71 (71 - 17) = 54 9 x 6 5 + 4 = 9

In each case the difference is divisible by 9 and the sum is always 9

Puzzle

•You are at a fountain and have with you a three gallon jug and a five gallon jug.

•The jugs have no markings on the sides. How would you be able to measure out exactly one gallon of water?

Solution•First, fill up the 3 gallon jug to the top, and pour it into the 5 gallon jug. 5 - 3 = 2 free gallons

left in the 5 gallon jug. Now, fill up the 3 gallon

jug again, and pour as much as you can into

the 5 gallon jug. 3 - 2 = 1 gallon of water left in

the 3 gallon jug. Finally, pour the remaining

gallon of water from the 3 gallon jug into your

1 gallon jug. Result = 1 gallon of water

We hope you’ve learnt something

new today...