#21
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Re: Plagiarism!
Heh, that's pretty cool. I never read that post since it was the last in the thread.
<font color="white">Alright, that's a lie. The minute I saw your post I decided to wait 3 months and claim the idea as my own to ascend to my rightful throne as lord of the OOT math nerds.</font> |
#22
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Re: Cool math shortcuts
That triangle with all the numbers is pretty cool. Pretty useful too
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#23
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Re: Cool math shortcuts
you can take a common way to solve squares and go one step further and make it easy to multiply numbers that aren't the same but are close to each other using an anchor. for example, to square 47 you square 50 to get 2500, subtract 3*100, and then add 9. so you get 2209. and you used the formula:
x^2 = a^2 + (x-a)(2a) - (x-a)^2 'a' can be anything but you pick a multiple of 10 to make it easy to do in your head. someone else referred to the way feynman described how to do squares near 50 in your head and this is feynman's way, but describing it in this formula shows that the number doesn't need to be near 50. so for example, to get the square of 38 in your head: 40^2=1600 subtract 2*80=160 and you get 1440 add 2^2=4 and you get 1444 but the formula above is specific to squares you can go back a step and make it easy to multiply numbers that are close but not the same. so if you want to multiply x times y, and 'a' is your anchor number: x*y = a^2 + (x-a)*a + (y-a)*a + (x-a)(y-a) yes this seems complicated but it's the same as feyman's way of squaring but you just add 2 steps. so to multiply 48*45 in your head: 50^2=2500 subtract 2*50=100 and get 2400 subtract 5*50=250 and get 2150 add 2*5=10 and get 2160. it might take some practice but this is the best way i have found, and after awhile you don't have to think about it too much. |
#24
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Re: Cool math shortcuts
Mulitply any 2-digit number ab by 11 and it's a(b+a)b
Example: 12*11 = 1(1+2)2 = 132 17*11 = 1(1+7)7 = 187 39*11 = 3(3+9)9 = 429 |
#25
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Re: Cool math shortcuts
Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100.
1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... |
#26
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Re: Cool math shortcuts
most of you know the shortcuts for figuring out if a whole number is divisible by:
2 - if it's even 3 - if the sum of the digits is divisble by 3 4 - if the last two digits are divisible by 4 5 - if the last digit is 0 or 5 6 - if it's divisible by 2 and 3 (duh) 8 - if the last 3 digits are divisible by 8 9 - if the sum of the digits is divisible by 9 but no one ever told me one for 7, and i thought that was bullshit, so i found it myself: write the number in question backwards under this number write the number 132645132645132645... now multiply each digit with the number below it, then add them all together if this number is divisible by 7, then the original is so, lets say you wanted to know if 27351223 was divisible by 7, well... 2*1+7*3+3*2+5*6+1*4+2*5+2*1+3*3=84, and 84 is divisible by 7, so 27351223 is divisible by 7 also not that you can't figure out if your new number is divisible by 7, repeat the procss: 4*1+8*3=28 which is divisible by 7, so 84 is too this methods kinda blows though, it's not as easy as the other ones, which is probably why they don't teach it |
#27
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Re: Cool math shortcuts
[ QUOTE ]
Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100. 1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... [/ QUOTE ] Good job Gauss. |
#28
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100. 1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... [/ QUOTE ] Good job Gauss. [/ QUOTE ] well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img] |
#29
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100. 1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... [/ QUOTE ] Good job Gauss. [/ QUOTE ] well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img] [/ QUOTE ] Gauss came up with it when he was five. |
#30
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Re: Cool math shortcuts
[ QUOTE ]
Gauss came up with it when he was five. [/ QUOTE ] I wonder if this story is apocryphal or not. But at any rate, if this is the old Gauss learns his teacher good, he was ten, I believe. |
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