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

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7/10/2018 9:02:45 AM

Hi Todd! On Tue, 10 Jul 2018 02:02:45 -0700 ToddAndMargo <ToddAndMargo@zoho.com> wrote: > Hi All, >=20 > Remembering from my school days, a famous mathematician > whose name I forget came up with a formula as a kid > that made math history. >=20 See https://en.wikipedia.org/wiki/Arithmetic_progression . They tell this s= tory about https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss - see http://www.coolmath.com/algebra/19-sequences-series/06-gauss-problem-arithm= etic-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. >=20 > Seems he had discovered that if you laid the number > out forward, then reverse underneath >=20 > N=3D5 >=20 > 1 + 2 + 3 + 4 + 5 =3D 15 > 5 + 4 + 3 + 2 + 1 =3D 15 > --------------------- > 6 6 6 6 6 =3D 30 >=20 > If you add the columns, you always got N+1 and N times. > And that make the formula >=20 > 1+2+3..N =3D (N+1)*N/2 >=20 > I always have fun recreating this formula from the > forward and reverse tables added as columns. >=20 > So feed the following an integer and have fun! >=20 > Yup. He blew his teacher's mind! >=20 > -T >=20 >=20 > $ echo "5" | p6 'my $N=3Dslurp(); say $N*($N+1)/2;' > 15 >=20 > $ echo "6" | p6 'my $N=3Dslurp(); say $N*($N+1)/2;' > 21 >=20 > $ echo "100" | p6 'my $N=3Dslurp(); say $N*($N+1)/2;' > 5050 --=20 ----------------------------------------------------------------- Shlomi Fish http://www.shlomifish.org/ Chuck Norris/etc. Facts - http://www.shlomifish.org/humour/bits/facts/ I=E2=80=99d love to change the world, but they won=E2=80=99t give me the so= urce code. =E2=80=94 Unknown Please reply to list if it's a mailing list post - http://shlom.in/reply .

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7/10/2018 9:47:29 AM

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-:+-$"-g&&print$_.$/}

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7/10/2018 9:55:03 AM

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 real 0m0.213s user 0m0.250s sys 0m0.032s ~ $ time perl6 -e 'say [+] 1..10000000000000000000' 50000000000000000005000000000000000000 real 0m0.198s user 0m0.236s sys 0m0.034s

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7/10/2018 10:42:50 AM

On 07/10/2018 02:47 AM, Shlomi Fish wrote: > Hi Todd! > > On Tue, 10 Jul 2018 02:02:45 -0700 > ToddAndMargo <ToddAndMargo@zoho.com> 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.

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7/10/2018 8:53:42 PM

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 > > real 0m0.213s > user 0m0.250s > sys 0m0.032s > > ~ $ time perl6 -e 'say [+] 1..10000000000000000000' > 50000000000000000005000000000000000000 > > real 0m0.198s > user 0m0.236s > 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.

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7/10/2018 8:55:49 PM

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 >

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7/11/2018 4:25:37 AM

> 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.=C2=A0 It took him only a few minutes.=C2=A0 They thought >> he cheated, so they sent him back with an even larger >> number to add up.=C2=A0 Same couple of minutes.=C2=A0 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=3D5 >> >> 1 + 2 + 3 + 4 + 5 =3D 15 >> 5 + 4 + 3 + 2 + 1 =3D 15 >> --------------------- >> 6=C2=A0=C2=A0 6=C2=A0=C2=A0 6=C2=A0=C2=A0 6=C2=A0=C2=A0 6 =3D 30 >> >> If you add the columns, you always got N+1 and N times. >> And that make the formula >> >> =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1+2+3..N =3D (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.=C2=A0 He blew his teacher's mind! >> >> -T >> >> >> $ echo "5" | p6 'my $N=3Dslurp(); say $N*($N+1)/2;' >> 15 >> >> $ echo "6" | p6 'my $N=3Dslurp(); say $N*($N+1)/2;' >> 21 >> >> $ echo "100" | p6 'my $N=3Dslurp(); 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=3D5 would be 1+2+3+4+5 --=20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Computers are like air conditioners. They malfunction when you open windows ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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7/11/2018 6:13:26 AM