Hi all, In "Makers of Mathematics" by Stuart Hollingdale there is a reference about Pythagoreans who where in the habit of representing numbers by pebbles in the sand.
Figure 2.1 illustrates how square numbers can be generated by adding successive odd numbers. ───────┐ o o o o│ ─────┐ │ o o o│o│ ───┐ │ │ o o│o│o│ ─┐ │ │ │ o│o│o│o│ The sum of first n odd numbers is simply n^2. How about some J code to generate figure 2.1 ? On Tue, May 15, 2018 at 5:22 AM, 'Jon Hough' via Programming < [email protected]> wrote: > Try this: > > smodd1=:+/@:>:@:+:@:i. > > Your tacit verb was creating forks, as can be seen with dissect: > load 'debug/dissect' > dissect '+/1+2*i. 5' > > > But since the sum of the first N odd numbers is N^2 > it is easiest to write > smodd=: *: > > > -------------------------------------------- > On Tue, 5/15/18, Skip Cave <[email protected]> wrote: > > Subject: [Jprogramming] Summing odd numbers > To: "[email protected]" <[email protected]> > Date: Tuesday, May 15, 2018, 5:29 PM > > A simple Quora question wants to know the > formula to sum the first n odd > numbers. > > I can write an explicit verb: > > smodd =.3 :'+/1+2*i.y' > > smodd 5 > > 25 > > I want to write a tacit verb: > > smodd1=:+/1+2*i. > > smodd1 5 > > 6 8 10 12 14 > > What am I doing wrong? > > > Skip Cave > Cave Consulting LLC > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
