Re: Applications of Mathematics

Toni Lassila wrote:

This is not possible. The golden ratio is irrational,
and can therefore not be calculated to arbitrary
precision using floating-point arithmetic. Therefore
it is clearly nonsense. It should be purged from
scientific mathematics.

Dave L. Renfro wrote:

What is the significance of floating-point arithmetic
for determining mathematical nonsense? Why not use
"exact integer arithmetic plus radicals", where the
golden ratio can be calculated to arbitrary precision?

R.G. Vickson wrote:

This sounds wrong. It can be computed to arbitrary precision:
just name a precision, and it can be calculated to that
accuracy and better. Of course, it cannot be computed to
_unlimited_ precision, but then neither can the fraction
1/5 on a standard computer that uses binary computations.

Yeah, I agree, although "unlimited" sounds like the same
thing to me as "arbitrary", but maybe "unlimited" is a
technical term in computer science that means "exact".

Personally, the fact that it's equal to (1/2) + (1/2)*sqrt(5)
(hence a quadratic irrational with a minimal polynomial of
x^2 - x - 1) is far more mathematically significant than
knowing it's approximately equal to 1 + 6/10 + 1/100 + 8/1000.
In fact, the golden ratio has a number of mathematically
significant properties that no floating-point arithmetic
computation would reveal. For example, its continued
fraction expansion is the slowest converging such expansion
among all irrational numbers (besides rational coefficient
affine images of the golden ratio). Of course, I'm
sure most everyone here knows these things, including
Toni Lassila, who I realize now was probably mocking
some sci.math trolls . . .

Dave L. Renfro

.

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