Re: Noah's List

*To*: mathgroup at smc.vnet.net*Subject*: [mg5712] Re: Noah's List*From*: Hans Havermann <haha at astral.magic.ca>*Date*: Sat, 11 Jan 1997 14:29:08 -0500*Sender*: owner-wri-mathgroup at wolfram.com

I wrote: >I have two lists, x and y, each containing n elements. I would like to >generate a new list, {{x[[1]],y[[1]]}, {x[[2]],y[[2]]},... >{x[[n]],y[[n]]}}, but have been unable to figure out a shorthand for it. A collective thank you to the (currently 14) people who responded to this. Transpose[{x,y}] was the most common suggestion with Thread[{x,y}] a distant second. Also offered were MapThread[List,{x,y}] and Table[{x[[k]],y[[k]]},{k,1,Length[x]}]. I am using the function to investigate the "square root" spiral, calculated and drawn by Robert Stanley Beard some 40 years ago [See "Patterns in Space", Creative Publications (1973), p.209]. The spiral may be thought of as the concatenation of triangles with sides 1, n^(1/2), and (n+1)^(1/2), for n=1 to infinity. angle[n_]:=ArcTan[1/n^(1/2)] x[n_]:=Range[n]^(1/2)*Cos[FoldList[Plus,0,angle[Range[n-1]]]] y[n_]:=Range[n]^(1/2)*Sin[FoldList[Plus,0,angle[Range[n-1]]]] z[n_]:=Transpose[{x[n],y[n]}] sets up the data points as *exact* expressions. ListPlot[z[111],PlotJoined->True,AspectRatio->Automatic] will draw 3 revolutions of the spiral, omitting the triangles' spokes to the origin. Thank you again. -- HaHa Rarebit Dreams