GeoGebra unearths a surprising aspect to Pythagoras' Theorem!

Wednesday 3 February 2016, 12:10PM
By Learn Implement Share

We all learnt about Pythagoras’ theorem at school, right? Take a right-angled triangle. Make a square each side. The area of the square on the longest side equals the sum of the other two areas. But did you know the same principle applies not just to squares but to any regular polygon?

To some readers this will be fascinating. However, the point of this article is that the free application GeoGebra enables students to make ‘discoveries’ such as this with relative ease. Why? Because when students start investigating some ‘maths’ with GeoGebra they start asking the ‘I wonder what would happen if … ’ questions.

The dynamic demonstrations featured here are of a GeoGebra file - featuring the ‘Pythagorean curiosity’ - being manipulated.  Don't miss the dynamic demos!

GeoGebra is the most widely used dynamic geometry software available today. It is staggeringly powerful software and contains the potential to revolutionise a maths teacher’s classroom yet with minimal requirement for a change in the teacher’s style. (A very rare feat for any application, resource or new strategy!) GeoGebra ought to be one of the most commonly used tools in every maths teacher’s toolkit.

A more extensive article, 'A Pythagoras investigation using geogebra' can be accessed here.      

If you are a New Zealand Yr 5 - 12 maths teacher and would like to become proficient with GeoGebra  and experience its wonders then there is a course for you. ‘Dynamic Geometry and Algebra with GeoGebra’ is an extensive online learning journey and has been running in Australia since 2009. The course is brought to you by Learn Implement Share. Learn Implement Share is now based in New Zealand. 

This is the best and most relevant PD I have ever done. The fact that it ran over a longer period of time gave me the opportunity to apply what I had learned to the subjects I was teaching. I have done single day PD's on computer software before, but once you are back in the classroom it is difficult to find the time to apply what you have learned while it is still fresh in your memory. Many of our senior students (now) use GeoGebra for their assignments as well. GeoGebra is also invaluable to demonstrate rules for Geometry and Trigonometry to students. Anne Redman, Corinda State High School, Queensland, 21.9.14 (2012 participant)