Re: An interesting math formula to share
On 2018-07-10 2:02 AM, ToddAndMargo wrote: Hi All, Remembering from my school days, a famous mathematician whose name I forget came up with a formula as a kid that made math history. As it transpires, when in school, they disciplined him by making his count all the number from 1 to some large number. It took him only a few minutes. They thought he cheated, so they sent him back with an even larger number to add up. Same couple of minutes. Blew his teacher's minds every number they gave him. Seems he had discovered that if you laid the number out forward, then reverse underneath N=5 1 + 2 + 3 + 4 + 5 = 15 5 + 4 + 3 + 2 + 1 = 15 - 6 6 6 6 6 = 30 If you add the columns, you always got N+1 and N times. And that make the formula 1+2+3..N = (N+1)*N/2 I always have fun recreating this formula from the forward and reverse tables added as columns. So feed the following an integer and have fun! Yup. He blew his teacher's mind! -T $ echo "5" | p6 'my $N=slurp(); say $N*($N+1)/2;' 15 $ echo "6" | p6 'my $N=slurp(); say $N*($N+1)/2;' 21 $ echo "100" | p6 'my $N=slurp(); say $N*($N+1)/2;' 5050 On 07/10/2018 09:25 PM, Darren Duncan wrote: > Your saying "count all the number" is confusing and doesn't seem to > relate to what follows. Did you mean to say "sum all the number"? -- > Darren Duncan > Yes, sum them. N=5 would be 1+2+3+4+5 -- ~~ Computers are like air conditioners. They malfunction when you open windows ~~
Re: An interesting math formula to share
Your saying "count all the number" is confusing and doesn't seem to relate to what follows. Did you mean to say "sum all the number"? -- Darren Duncan On 2018-07-10 2:02 AM, ToddAndMargo wrote: Hi All, Remembering from my school days, a famous mathematician whose name I forget came up with a formula as a kid that made math history. As it transpires, when in school, they disciplined him by making his count all the number from 1 to some large number. It took him only a few minutes. They thought he cheated, so they sent him back with an even larger number to add up. Same couple of minutes. Blew his teacher's minds every number they gave him. Seems he had discovered that if you laid the number out forward, then reverse underneath N=5 1 + 2 + 3 + 4 + 5 = 15 5 + 4 + 3 + 2 + 1 = 15 - 6 6 6 6 6 = 30 If you add the columns, you always got N+1 and N times. And that make the formula 1+2+3..N = (N+1)*N/2 I always have fun recreating this formula from the forward and reverse tables added as columns. So feed the following an integer and have fun! Yup. He blew his teacher's mind! -T $ echo "5" | p6 'my $N=slurp(); say $N*($N+1)/2;' 15 $ echo "6" | p6 'my $N=slurp(); say $N*($N+1)/2;' 21 $ echo "100" | p6 'my $N=slurp(); say $N*($N+1)/2;' 5050
Re: An interesting math formula to share
On 07/10/2018 03:42 AM, Brian Duggan wrote: On Tuesday, July 10, ToddAndMargo wrote: $ echo "5" | p6 'my $N=slurp(); say $N*($N+1)/2;' 15 $ echo "6" | p6 'my $N=slurp(); say $N*($N+1)/2;' 21 $ echo "100" | p6 'my $N=slurp(); say $N*($N+1)/2;' 5050 Another cool thing is that this formula is used in Perl 6 under the hood to calculate the sum of the integers in a range instantly: ~ $ time perl6 -e 'say [+] 1..100' 5050 real0m0.213s user0m0.250s sys 0m0.032s ~ $ time perl6 -e 'say [+] 1..1000' 500500 real0m0.198s user0m0.236s sys 0m0.034s Fascinating! If I ever get bored and try to figure out by hand how to do an inverse cosine, some come smack me.
Re: An interesting math formula to share
On 07/10/2018 02:47 AM, Shlomi Fish wrote: Hi Todd! On Tue, 10 Jul 2018 02:02:45 -0700 ToddAndMargo wrote: Hi All, Remembering from my school days, a famous mathematician whose name I forget came up with a formula as a kid that made math history. See https://en.wikipedia.org/wiki/Arithmetic_progression . They tell this story about https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss - see http://www.coolmath.com/algebra/19-sequences-series/06-gauss-problem-arithmetic-series-01 , but the formula for that predates him by many centuries. "The" gauss! I was an RF (Radio Frequency) Design Engineer before becoming a computer consultant (couldn't find work in RF Design after the end of the cold war with all the outsourcing that occurred). "Gauss" was a real big deal.
Re: An interesting math formula to share
On Tuesday, July 10, ToddAndMargo wrote: > $ echo "5" | p6 'my $N=slurp(); say $N*($N+1)/2;' > 15 > > $ echo "6" | p6 'my $N=slurp(); say $N*($N+1)/2;' > 21 > > $ echo "100" | p6 'my $N=slurp(); say $N*($N+1)/2;' > 5050 Another cool thing is that this formula is used in Perl 6 under the hood to calculate the sum of the integers in a range instantly: ~ $ time perl6 -e 'say [+] 1..100' 5050 real0m0.213s user0m0.250s sys 0m0.032s ~ $ time perl6 -e 'say [+] 1..1000' 500500 real0m0.198s user0m0.236s sys 0m0.034s
Re: An interesting math formula to share
Hi Todd! On Tue, 10 Jul 2018 02:02:45 -0700 ToddAndMargo wrote: > Hi All, > > Remembering from my school days, a famous mathematician > whose name I forget came up with a formula as a kid > that made math history. > See https://en.wikipedia.org/wiki/Arithmetic_progression . They tell this story about https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss - see http://www.coolmath.com/algebra/19-sequences-series/06-gauss-problem-arithmetic-series-01 , but the formula for that predates him by many centuries. > As it transpires, when in school, they disciplined him by > making his count all the number from 1 to some large > number. It took him only a few minutes. They thought > he cheated, so they sent him back with an even larger > number to add up. Same couple of minutes. Blew his > teacher's minds every number they gave him. > > Seems he had discovered that if you laid the number > out forward, then reverse underneath > > N=5 > > 1 + 2 + 3 + 4 + 5 = 15 > 5 + 4 + 3 + 2 + 1 = 15 > - > 6 6 6 6 6 = 30 > > If you add the columns, you always got N+1 and N times. > And that make the formula > > 1+2+3..N = (N+1)*N/2 > > I always have fun recreating this formula from the > forward and reverse tables added as columns. > > So feed the following an integer and have fun! > > Yup. He blew his teacher's mind! > > -T > > > $ echo "5" | p6 'my $N=slurp(); say $N*($N+1)/2;' > 15 > > $ echo "6" | p6 'my $N=slurp(); say $N*($N+1)/2;' > 21 > > $ echo "100" | p6 'my $N=slurp(); say $N*($N+1)/2;' > 5050 -- - Shlomi Fish http://www.shlomifish.org/ Chuck Norris/etc. Facts - http://www.shlomifish.org/humour/bits/facts/ I’d love to change the world, but they won’t give me the source code. — Unknown Please reply to list if it's a mailing list post - http://shlom.in/reply .
Re: An interesting math formula to share
Hi!
On Tue, Jul 10, 2018 at 02:02:45AM -0700, ToddAndMargo wrote:
> Remembering from my school days, a famous mathematician
> whose name I forget came up with a formula as a kid
> that made math history.
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss
greetings,
domm
--
#!/usr/bin/perl http://domm.plix.at
for(ref bless{},just'another'perl'hacker){s-:+-$"-g&$_.$/}
An interesting math formula to share
Hi All, Remembering from my school days, a famous mathematician whose name I forget came up with a formula as a kid that made math history. As it transpires, when in school, they disciplined him by making his count all the number from 1 to some large number. It took him only a few minutes. They thought he cheated, so they sent him back with an even larger number to add up. Same couple of minutes. Blew his teacher's minds every number they gave him. Seems he had discovered that if you laid the number out forward, then reverse underneath N=5 1 + 2 + 3 + 4 + 5 = 15 5 + 4 + 3 + 2 + 1 = 15 - 6 6 6 6 6 = 30 If you add the columns, you always got N+1 and N times. And that make the formula 1+2+3..N = (N+1)*N/2 I always have fun recreating this formula from the forward and reverse tables added as columns. So feed the following an integer and have fun! Yup. He blew his teacher's mind! -T $ echo "5" | p6 'my $N=slurp(); say $N*($N+1)/2;' 15 $ echo "6" | p6 'my $N=slurp(); say $N*($N+1)/2;' 21 $ echo "100" | p6 'my $N=slurp(); say $N*($N+1)/2;' 5050
