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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 son Joshua is currently in year 11 preparing for the HSC. Josh was doing reasonably well in mathematics and yet we felt, and his teachers agreed, that if he really applied himself he could be achieving much better results. We asked around for a maths tutor and Graeme Henderson came highly recommended. Joshua began to see Mr Henderson one hour per week and from the very first week Joshua’s motivation escalated. His maths improved to the point where he is now often achieving 100% in his exams, he applies himself to do hours of homework, something he had rarely done in the past, but most of all Josh has found a love of mathematics. Maths is no longer a chore. I believe this all stems from Mr Henderson’s gifted ability not only as a teacher, also as an encourager and motivator. I get motivated just listening to them! Josh told us this week that he wishes he could be tutored every day after school. When the results come through from Joshua’s exams, he is delighted and this has inspired him to become motivated to spend much more time applying himself to his other subjects. Josh is working hard to gain a great result in his HSC. I can personally recommend Mr Henderson as a truly wonderful tutor.
Deborah B (Parent, 2012)

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