Transition Year Maths PROJECT 6.3 Sequence of Squares and right-angled Triangles


Continue on this sequence for 50 terms and find 4 different right-angled triangles which are not multiples of each other.


12 22 32 42 52 62 72 82


1 4 9 16 25 36 49 64 \/ \/ \/ \/ \/ \/ \/ 3 5 7 9 11 13 15


32 52 –42 = 32


Subtract each successive square from the previous one. This gives an odd number, but every so often, one of these odd numbers is itself a square. Therefore 52


–42 = 32 gives 32 + 42 = 52 .


There are three more to be found before 502


is reached!


Pythagoras: Greek mathematician, 600 BC


Pythagoras loved truth and wisdom and spent his life searching for these qualities, often by studying numbers. He founded a secretive religious group devoted to the study of numbers. This group believed numbers were the ultimate reality, and everything could be predicted by studying them. It is suspected that the concept of irrational numbers was first discovered by this group but it was so abhorrent to their search for truth that they denied the existence of such numbers. Pythagoras was one of the first philosophers to suggest that the thought process was carried out in the brain, not the heart.


Questions


The following Questions pages are FREE to download from mentorbooks.ie/resources


1. Study the numbers between 20 and 30 and identify which are defective, slightly defective, perfect and excessive (Hint: there is one perfect number between 20 and 30). ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________


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