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Geometry Expressions Newsletter
Geometry Expressions Newsletter

October 2010
Indeterminate numbers of sides
Generic n-gon
Ngon angle
Geometry Expressions allows you to make quantities such as length, angle, radius, etc. indeterminate.  These indeterminates show up in mathematical expressions for output measurements.
 
Geometry Expressions 2.2 extends this concept to allow two types of object with an indeterminate number of sides.  These are:
  • n-gon
  • curve approximation
While the drawing uses a specific value for n, measurements retain the generic value.
How to...measure the area between curves
Curve sided polygon
There is a trick to measuring the area between two curves.

You can create an arc lying between two points on any curve.  But (with the exception of circles) GX will not let you put a point on the intersection of two curves.

So we resort to the trick of joining two arcs by line segments then making the ends of the segments lie on the intersection points. 

Here's how:

First create an arc between two points on the first curve and between two points on the second curve. Join the ends of the two arcs by line segments and create a polygon from the two arcs and the two segments.

Now use Constrain / Proportional to specify the parametric location of the vertices on the two curves so they lie at the intersections.

Area between curves
Problem of the Month
Paper Cone
A cone is made from a paper circle by cutting out a sector and taping the edges.

What is the angle at the apex of the cone with the largest volume which you can make in this way from a given paper circle?

Have you seen this angle before?
[Hint:  think Chemistry]
 
GX Books
Farmer and the Mathematician
The latest Geometry Expressions book is
The Farmer and the Mathematician by award winning teacher Larry Ottman.

This book explores mathematical modeling in the context of central pivot irrigation
 
Check out this and the other GX books
here
 
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