Whole number generators

[Video to come]

Overview

Whole number sequences occur commonly in science and mathematics.

Two of the best known are:

• the powers of 2: 1, 2, 4, 8, 16, 32, 64 ,128 ,256, 512, 1024, … in which each term in the sequence, after the first,  is obtained by simply doubling the previous term;
• the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34 ,55, 89, .. in in which each term in the sequence, after the first two, is obtained by adding the previous two terms.

These sequences, generated by simple rules, not only commonly occur in mathematical and scientific work but seem to exert a counting fascination for people, both young and experienced.

In this course we will delve into some of the delights, peculiarities, and mysteries of whole number sequences, and the processes by which they are generated.

Our approach will be to think of number sequences as being produced by whole number generating “machines”, each of which has some internal configuration to produce a sequence of whole numbers.

Lessons

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1.1 Powers of 2

1.2 Fibonacci numbers

1.3 Linear sequences

1.4 Quadratic sequences

1.5 Differencing

1.6 Summing

1.7 Connections between differencing and summing

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