Math Illustrations Tips
 May 2011
 We're on the web at www.mathillustrations.com.Tips this month:  exterior and interior angles, constraints and constructions, working with pictures.
 Exterior and interior angles [Video] When you ask Math Illustrations to display the angle between two line segments (Calculate/Angle), it will initially give you the interior angle. If you want the exterior angle you have two choices: Select the segments again and Calculate/Angle, Math Illustrations will give you one of the exterior angles. (If you keep pressing Calculate/Angle, you will get all 4 possible angles)Select the angle symbol and drag it into the desired quadrant.
 Constraints and Constructions [Video] Users with experience of construction based geometry systems sometimes overlook easy ways to use constraints to do tasks. For example, let's say you want a circle through 3 specific points.  Here's what you need to do:Draw the 3 points and constrain their coordinates.Draw a circle with some arbitrary center and whose circumference point is one of the 3 points (point A in our diagram).Select point B, hold down the shift key and select the circle, then use Constrain / Incident.Select point C, hold down the shift key  and select the circle and use Constrain / Incident.  Try applying the same approach to create an ellipse through 5 points.  [Video]
 Pictures [Video] To add an image to a Math Illustrations diagram:Choose Draw / Picture from the menu.Click and drag a rectangle which will contain the picture.Navigate to the picture file you want to insert.    Once you have inserted your picture you can select it and use the context menu to change its transparency, so the axes and grid shows through. You can also Pin or Unpin the drawing.  Pinning is relative to the page, rather than relative to the axes.  Unpinned pictures move with geometry when you pan.     Our picture is of an Archimedes trammel (a tool for drawing ellipses).  Initially the drawing is pinned and allows you to drag the axes relative to the drawing, and position them at the center of the trammel.The geometry of the drawing can be modeled with an ellipse.