# squares telescoping

lawrence shared this question 4 years ago

need to make series of squares where ratio of lengths of consecutive squares =2:1; and find the sum of the perimeters/length of first n terms of the squares. Any insight or help is much appreciated.Thanks

I think the IterationList is very useful. like this:

IterationList[Translate[Dilate[t, 1 / 2, Point[t, 0]], Vector[Point[t, 0], Point[t, 1 / 2]]], t, {poly1}, n - 1]

(list1 is squares, list2 is for lines(set filling transparent).

good luck!

1

I think the IterationList is very useful. like this:

IterationList[Translate[Dilate[t, 1 / 2, Point[t, 0]], Vector[Point[t, 0], Point[t, 1 / 2]]], t, {poly1}, n - 1]

(list1 is squares, list2 is for lines(set filling transparent).

good luck!

1

Perfect!

1

W.r.t. earlier posting 'triangle series' ,need to know how to change the GenPair tool from 3 parameters to 1 parameter(point D as input) by appending segments DE and EF to a polyline which can be used as output( together with point F).

Any insight or help very much appreciated . Thanks again!

1

to get a list, input this command:

1. listOutput: {Segment[D, E], Segment[E, F]}

and then you select listOutput from dropdown list for output custom tool

1

Hi,

Consider using Sequence command to generate list of squares.

Appear to have less clutter as less objects are generated in the Algebra list

Can access the area, perimeter, etc using list commands

See example file.

Best Regards,

lewws