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This is a strategy to find out the length of a missing side on a right triangle.
e.g.
Here is the formula
In a right angled triangle the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
The hypotenuse is the line that is opposite the right angle.
Discovered by Rebecca
Lattice multiplication is another way to do multiplication. It is actually very similar to using Algorithms to work it out, noticing that you have to multiply each number by each number which is exactly the same with algorithms except in this case you don’t have to carry it over and that you have to add everything up once you are done.
How to do lattice multiplication:
Draw up a box with the number of squares that you need for your multiplication problem. If it was 5945 X 6734 you would have 4×4, and likewise if you have 932 X 576 is would be 3×3
2. Once you have done this you must go around every square doing the multiplication in it. You must write the tens in the top left corner and the ones in the bottom left corner.
3. Then extend the lines that are going diagonally across bringing them out of the box in the bottom left corner.
4. Then starting from the bottom right area inside the diagonals, go clockwise around the square adding up the numbers. (Remember to carry the tens as you go round.
5. The answer is the figure that you just insert in the diagonals going anti clockwise this time from the top left.
Discovered by Zachary
The value of pi with first 100 decimal places is: 3.1415926535897932384626433832795028841971693993751058209749445923078164
062862089986280348253421170679
‘Pi’ is the 16 letter in the greek alphabet
An ancient mathematician Archimedes of Syracuse who lived between 287 – 212 BC derived the value of pi based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed.
A German mathematician, Ludolph van Ceulen, devoted his entire life to calculate the first 35 decimal places of pi.
The first 144 digits of pi add up to 666 and 144 = (6+6) x (6+6).
William Shanks (1812-1882) worked for years manually to find the first 707 digits of pi. Unfortunately, he made a mistake after the 527th place and the following digits were all wrong.
”Pi Day” is celebrated on March 14 (which was chosen because it resembles 3.14). The official celebration begins at 1:59 p.m., to make an appropriate 3.14159 when combined with the date. Albert Einstein was born on Pi Day (3/14/1879) in Ulm Wurttemberg, Germany.
William Jones (1675-1749) introduced the symbol “π” in 1706
The first six digits of pi (314159) appear in order at least six times among the first 10 million decimal places of pi.
A website called the pi search page http://www.angio.net/pi/piquery finds numbers such as your birthday in the first 100 million digits of pi
Discovered by Praharsh
How to do Odd Magic Squares (This has a pattern)
This works with ANY odd numbers (e.g. 3×3, adding up to 15 on every row, column and diagonal, the numbers are from no.1 to 9).
This is a 5×5 magic square, all rows, columns and diagonals add up to 65, the numbers are from 1 to 25.
Discovered by Gabriel
The Beauty of Mathematics
Sequential Inputs of numbers with 8
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
Sequential 1′s with 9
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111
Sequential 8′s with 9
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Numeric Palindrome with 1′s
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
Without 8
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999
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 = 999998000001
9999999 x 9999999 = 99999980000001
99999999 x 99999999 = 9999999800000001
999999999 x 999999999 = 999999998000000001
Sequential Inputs of 6
6 x 7 = 42
66 x 67 = 4422
666 x 667 = 444222
6666 x 6667 = 44442222
66666 x 66667 = 4444422222
666666 x 666667 = 444444222222
6666666 x 6666667 = 44444442222222
66666666 x 66666667 = 4444444422222222
666666666 x 666666667 = 444444444222222222
Discovered by Fletcher
We are a new mathex group this year and we are eagerly making our new discoveries.
Follow our maths discoveries here – we hope you are as excited as we are.
This is another method of working out multiplication problems.
1. Draw a box. The number of squares in the rows and columns depend on the number of digits in the problem.
e.g. 89×83
2. Draw in the diagonals in each square.
3. Do the multiplication for each area, putting the digits into the separate boxes. (The tens go into the right corner of the box and the ones go into the left corner of the box).
e.g.
Then extend the diagonals
and total up each diagonal column starting with the right and moving towards the left. Put the ones total into the diagonal and carry over the tens (or more).
Therefore 89×63=5607
Discovered by Clinton
Welcome to Y7 Mathex Class of 2010 »« How To Work Out Square Roots
The square root of the number ‘n’ can be written as √n or as n^1/2.
Square roots can be worked out by factorizing the number down to their prime factors
Write them as squared prime factors.
36 = 2 x 18
18 = 2 x 9
9 = 2 x 3
= 2 x 2 x 3 x 3
= 2^2 x 3^3
Take the prime factors only (without the exponent) and multiply them together.
This method only works with square numbers.
Discovered by Oliver
1. Think of a number.
2. Multiply by 3.
3. Add 1.
4. Multiply by 3 again.
5. Add the number you first thought of. The number should now end in 3.
6. Drop the 3. You are now left with the number you first thought of.
Amazing!
example
1. =7
2. =21
3. =22
4. =66
5. =73
6. =7
Discovered by Annis
“Sets” is an arithmetic problem when sets x and y are joined together (usually in a Venn diagram) to find another set z.
e.g. Out of 30 people eating at a restaurant, the choices for dessert were as follows:
17 ate fruit salad, 14 ate ice cream and 16 ate pavlova. 7 chose fruit salad and ice cream, 11 chose fruit salad and pavlova. 5 chose ice cream and pavlova and 2 had all three.
How many chose pavlova only, How many didn’t have dessert. How many chose ice cream only?
Way to solve:
pavlova only = 2, no dessert = 4, ice cream only = 4
Symbols:
discovered by Henry
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