| What Is Ardee? |
| Ardee is a tool for observing the strange world of repeating decimals. Remarkable number patterns often occur to the right of the decimal place when numbers don't divide evenly into another. This phenomenon has long been observed and investigated by number theorists, principally Leonhard Euler, who formulated a theorem and a function that explains and predicts some of this behavior. Ardee is a specialized calculator that allows you to directly observe the patterns in quotients carried out to almost any length to the right of the decimal.
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| The Story Behind Ardee |
I'm not a mathemetician. I was merely one of those (evidently rare) kids who discovered repeating decimals in the third grade and found them curious and mystifying. And when I asked my teachers why this odd phenomena happened I received frowns and shugs. (Frowns = Who cares? and shrugs = Who knows?) These weren't very satisfying answers but there it was.
Much later I found that others shared my curiousity and a few even attached mystical significance to it. For instance, the cyclical series of repeating decimals for the divisor 7 form part of the basis for Russian mathemetician Peter Ouspensky's enneagram, an occult symbol for the forces of creation in the universe. In more recent times, complex repeating decimals have formed the basis for advanced cryptographics. But it was really Karl Popper who revealed that mathmatics, though in one sense a human invention, is at the same time an undiscovered country with endless mysteries:
...we may invent a method of naming the natural numbers so that we can, in principle, always add one, and so go on to infinity. This is our invention, in this case belonging to the Babylonians. But from this invention there emerge unintended and unavoidable consequences that we neither invent, nor make, but discover. For example, that there are odd and even numbers; or that there are divisible numbers and prime numbers... These prime numbers have given rise to many solved and many more yet unsolved problems. [...] The very fact that a problem itself has to be discovered--and that there is ingenuity needed to discover a problem, and not only its proof--shows you that unintended consequences arise with the construction of the number system. [...]
Ardee is a sandbox for such discoveries as they relate to repeating decimals. Here you may pose fractions and see what happens. It may be that you discover patterns that will even lead to predictable rules. But for Ardee, there are no rules; there's simply discovery. I leave rule based approaches to mathemeticians.
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