Is infinity a number?

Friday 24 October 2014

Today I wanted to quickly convince my Maths SL students that for any triangle the ratio of the length of a side to the sine of the angle opposite it is always equal to the ratio of another side of the same triangle to the side opposite it - what we know as the Law of Sines (or Sine Rule). I used a sketch on the dynamic geometry software Geometers Sketchpad to do this. So, in front of the class (projected onto my whiteboard) I dragged around one of the vertices of a triangle and we watched to see what happened - observing that the three ratios (side length to sine of opposite angle) were always equal (measurements were updated dynamically in the sketch). It's fun to play with a dynamic image. One of my students 'played' with it and some of her classmates encouraged her to see what would happen if she tried to move a vertex so that the three vertices were collinear - thus, making it no longer a triangle but just a line segment (two of the angles having a measure of 0 degrees). What would happen? Watch the video below to see. Is infinity infinity a number?

   

But, infinity is not a number, but a concept.  Not easy to communicate to students.  Click here to listen to a clip from the BBC radio program The Infinite Monkey Cage - and you'll hear why it's not so easy to describe.


Tags: infinity, geometers sketchpad, law of sines


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