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Magical maths
- 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
- 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...