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Transcendental Nature of Pi

March 22, 1987

A few comments are in order about your editorial (March 15), "Pi-Eyed," on the record-setting computations of pi.

1--You state that pi is both transcendental and irrational. True, but redundant. All transcendental numbers are irrational. (The term transcendental means that a number cannot be a zero of a polynomial with integer coefficients.) The point is that the irrationality alone of pi guarantees a non-repeating decimal expansion.

2--Ten to the second power does not have 100 digits; it is equal to 100 and has precisely three digits. Likewise, 10 to the third power is 1,000 with four digits; 10 to the sixth power is 1 million, with seven digits. What you evidently meant was: a 100-digit expansion of pi (or any other number) can be expressed as having 10 to the second power digits, etc.

3--The question of the existence of the 10 to the 1-1,000th power of pi missed the point. The word exist, when referring to mermaids and unicorns, deals with the concept of tangible objects. But digits are abstract notions. They don't "exist" in the sense of being made of matter and occupying space. One cannot go out and find even the first few digits of pi lying around somewhere. However, any such digit is certainly calculable, given sufficient time. As with any entity having vast dimensions in space or time, our inability to ultimately perceive some specified digit of pi is not an issue of existence but simply a demonstration of the limitations of large numbers.

SKIP NEWHALL

Valencia

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