The Magical World of Patterns

Let's warm up with some background info of "number sequences":

"A number sequence is a set (represented by { }) of number arranged in order. It may terminate or continue indefinitely."
                                                                                             --N. Johnson

• Archimedian Spiral

Spirals are excellent visualization of number sequences. This particular spiral is called the Archimedian Spiral:

t_n represents the n^th (be it 1^st, 2^nd, 3^rd,...) number, or term, in the sequence.
The general rule, t_n=n, governs how the "sequence" is a "pattern". In this case, the value of the term is equal to the number of order the term comes in... In other words, the n^th term is equal to n:

Our "set" of sequence can be notated by the following:

{1,2,3,4,...}

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• Exponential Spiral

Here is another type of spiral, called the Exponential Spiral:

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Both of these spirals can go on forever, keeping the pattern described by the equation. They also occur in nature (take a look at seashells and the annual rings of trees), hence the sequences they represent are organic sequences. Patterns are certainly a big part of our lives!

Not only that they are visually pleasant, patterns are also handy when it comes to problem solving. For more on patterns, follow the navigation bar. As I've said before, by the time we've gone through all of the gardens on our map, math to you would be like honey!

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