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Iterations (Repetitions)

A cross section of a nautilus shell, showing the regular chambersMany things repeat.

When you learn to count … 1, 2, 3, 4, 5, … you are increasing your number by one every time.  Many number sequences are nothing more than always repeating the same algorithm.  When a creature produces its shell, it is repeating the same simple building instructions as it grows, thereby creating a spiral (or one shell of a bivalve).

On a semi-humorous, semi-serious note, the idea of a day that kept repeating itself formed the basis for the entertaining movie, Groundhog Day.

In this part of the website I want to help you explore such repeating things.




Sequences and Series ~ Repeating patterns with numbers

Mathematical Induction ~ Repeating patterns with ideas, concepts, and algebraic structures

Fractals ~ Repeating patterns with geometric shapes

Our daughter was tutored by Graeme as she was required to sit a maths exam, and complete a maths course, in order to attend college in the USA. Graeme came highly recommended as a brilliant tutor, and he definitely did not disappoint. As a parent of three adult children, I have accessed several tutors over the years, and none of them have come even close to being as helpful and skilful as Graeme. Our daughter, Michaela, particularly liked how Graeme could relate maths concepts to everyday situations, something that helped her immensely. Graeme has extensive knowledge in various areas of maths, and this knowledge combined with his patient, empathic manner, makes him the outstanding tutor that he is. Graeme went above and beyond what would be expected of a tutor. He was truly dedicated to our daughter’s learning and she could not have achieved her goals without him.
Gillian Q (parent, 2013)

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