median
don steward
mathematics teaching 10 ~ 16

Sunday, 28 January 2018

pythagorean triples

studying square numbers with two of them summing to a third (for integers) has interested various ancient and hopefully modern civilisations

this work develops some of the extensive ideas provided by Dr Ron Knott at Surrey University (many thanks to him)
Hannah Jones used these and other resources to devise classroom tasks for an EPQ project

pythagorean triple introduction ppt





















various patterns can be used to find pythagorean triples, those starting with an odd number being more commonly known

finding pythagorean triples ppt



















seeking pythagorean triples with a selected shortest side uses the difference of two squares and factor pairs

triples for a shortest side ppt






















a longer list of pythagorean triples is available at TSM resources

there are various formulae for finding pythagorean triples from a parameter (or two)
these provide primitive triples (without common factors) but not usually multiples of these

triple generators ppt



















the graphical work of Adam Cunningham and John Ringland (in the Wikipedia entry) on primitive pythagorean triples is interesting

graphing primitive triples ppt





















there are also some novel methods for generating triples from fractions, identified in Dr Ron Knott's work

fraction generators ppt




















some problems with lengths in triangles and rectangles, involving pythagorean triples

triangle lengths ppt



















a variety of problems, all involving the 3, 4, 5 triangle

3, 4, 5, problems ppt





















some problems on quadratic equations set up as pythagorean triples with various expressions for their lengths

expressions triples ppt


















the perimeters of pythagorean triple triangles have some interesting patterns

perimeters of triple triangles ppt





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