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lurey
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Posted on 06-07-07 9:15
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Beauty of Maths: 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 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 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 and finally take a look at this symmetry 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
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NepTalk
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Posted on 06-07-07 9:21
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raascal
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Posted on 06-07-07 2:06
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Chicago-Bull
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Posted on 06-07-07 3:26
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Very tricky math! (This must be done in your head only. DO NOT use paper and pencil or a calculator. Try it) Question:::::Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total? .............................................................. .................................................................... ............................................................................ .................................................................................. ANSWER:::Did you get 5000? The correct answer is actually 4100.Don't believe it? Check with your calculator! ;)
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lurey
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Posted on 06-07-07 3:41
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tregor
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Posted on 06-07-07 4:36
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i got 4100 whats the problem?
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Chicago-Bull
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Posted on 06-07-07 7:02
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blue_moon
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Posted on 06-07-07 7:34
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Bull doesn't know how to add.
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Chicago-Bull
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Posted on 06-07-07 7:44
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AznshawtY
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Posted on 06-07-07 7:47
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divdude
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Posted on 06-07-07 8:45
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Another Question. What is the size of largest square that can be inscribed in a unit cube? Note** The answer can be easily googled so the important thing is not the answer itself it is the process. Lets see how many unique processes can we see.
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blue_moon
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Posted on 06-07-07 9:09
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Square formed in diagonal of the cube.
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divdude
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Posted on 06-07-07 9:54
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@bluemoon close enough, now can you calculate the size too and post the method as well.
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propensity
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Posted on 06-07-07 11:27
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Even though I don't have an answer, I don't think blue_moon's answer is close enough. I will try to solve it. Good question.
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divdude
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Posted on 06-08-07 12:13
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gemmi_auj
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Posted on 06-08-07 12:58
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divdude, Let us consider a unit cube lying on a plane on one of its faces. When a vertical plane passing through a diagonal of the cube's horizontal faces is slowly rotated about a line that is parallel to the diagonal but passes through the center of the cube, a time will come when the intersection points of the plane and two pairs of diagonally opposite edges of the cube will exactly form a square. This will be the largest square that can be inscribed in the cube. If the plane intersects each of these edges at a distance of x from the diagonally opposite vertices of the cube, then for the intersection to be a square, x^2 + x^2 = (1-x)^2 + (1-x)^2 + 1 which implies x = 3/4. The length of each side of the square is then (3/4)*(2)^0.5. So the square's area will be 9/8.
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divdude
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Posted on 06-08-07 5:31
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@gemmi nice work. Very intuitive method. Fellas any more methods?
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blue_moon
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Posted on 06-08-07 7:03
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Thats the one I was saying
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lurey
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Posted on 06-08-07 7:07
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ok i think the beauty part was over after i posted my original stuff....all these are ugliness of maths :P
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divdude
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Posted on 06-08-07 7:40
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@lurey lol As they say beauty is in the eyes of beholder.
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