Geometer’s Sketchpad Sketches at Sketch Exchange

Before I became a GeoGebra user, I used The Geometer’s Sketchpad. I migrated to GeoGebra because aside from it is free, it is more friendly to students. Geometer’s Sketchpad requires a little mathematical maturity and knowledge of geometric constructions. I still like Geometer’s Sketchpad,  GeoGebra is getting and better.

geometer's sketchpad

Last month, I have shared to you more than 12000 free dynamic applets from GeoGebraTube and more than a year ago, I have also mentioned more than 7000 demonstrations from Wolfram. To add to the list of dynamic geometry resources, The Geometer’s Sketchpad has also created its library of “sketches” in Sketch Exchange.  Sketch Exchange as of this writing has more than 500 sketches available.  Just like GeoGebraTube and Wolfram Demonstrations, it is a place where GSP users can share sketches, tips, and tutorials.

Most of the sketches in Sketch Exchange requires Geometer’s Sketchpad 5.05, a free upgrade if you have Sketchpad 5.

Finding the General Formula for the kth Polygonal Number

If we represent numbers using “dots,” there are special numbers that can form “polygons.” Numbers that can form polygons are called polygonal numbers. For example, the square numbers 1, 4, 9, 16 and so on form a “square.”  As shown below, it is easy to see that the 10th square number is a square with 10 rows and 10 columns. This means that the 10th square number is equal to 100 (has 100 dots).

polygonal numbers

The Representation of Square Numbers

Like square numbers, triangular numbers form a shape. You guessed it right, the shape is a triangle. Finding the 15th triangular number seems hard, but we have already learned that triangular numbers are connected to the sum of the first m positive integers. The mth triangular number has

1 + 2 + 3 + \cdots + m = \frac{1}{2}m(m+1) dots. » Read more

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