This document discusses various mathematical concepts including: - The origins of mathematics in ancient Egypt and Babylonia and key developments in China, Greece, and the 16th century. - Types of special numbers like Armstrong numbers, properties of 666, vampire numbers, and palindromes using 1. - Mathematical tricks and patterns like multiplying by 9, the '11' rule, and the magic of the number 9. - A puzzle involving using a 3 gallon and 5 gallon jug to measure out exactly 1 gallon of water.

1. Magical Maths
Presented By:
Ben
Sian
Holly
Martin

2. 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.
-

3. What special things are there about maths...

4. Armstrong Numbers
Armstrong numbers involve squared
numbers.
E.g. 153 = 13 + 53 + 33
Some other Armstrong numbers are:
370, 371, 407

5. 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

6. Vampire Numbers
The number 1260 is a vampire
number...
With 21 and 60 as fangs
Since that 21 x 60 = 2160
Others are: 1395 = 15 x 93
1435 = 41 x 53
1530 = 51 x 30

7. Numeric Palindrome with
number 1
1 x 1 = 1
11 x 11 = 121
111 x 111 =12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

8. Sequential Inputs of 9
9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998001
9999 x 9999 = 99980001
99999 x 99999 = 9999800001
999999 x 999999 = 9999980000001
9999999 x 9999999 = 999999800000001
99999999 x 99999999 = 9999999000000001
999999999 x 999999999 = 999999990000000001

9. 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...

10. 3

11. The ’11’ Rule
Ever 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

12. However, this rule
will will only work
with numbers that
are as big as 9.

13. The Magic of 9
Table Sum of the digits of each product
1 x 9 = 9 0 + 9 = 9
2 x 9 = 18 1 + 8 = 9
3 x 9 = 27 2 + 7 = 9
4 x 9 = 36 3 + 6 = 9
5 x 9 = 45 4 + 5 = 9
6 x 9 = 54 5 + 4 = 9
7 x 9 = 63 6 + 3 = 9
8 x 9 = 72 7 + 2 = 9
9 x 9 = 81 8 + 1 = 9
10 x 9 = 90 9 + 0 = 9

14. 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

15. Puzzle
•Youareatafountainandhavewithyou
athreegallonjugandafivegallonjug.
•Thejugshavenomarkingsonthesides.
Howwouldyoubeabletomeasureout
exactlyonegallonofwater?

16. 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

17. We hope you’ve
learnt something
new today...