ELorenz wrote:When speaking about mathematics you have to be very careful about how you say things.
ELorez wrote:However it is not true that x^2 = 1/2*k*x^2.
ELorenz wrote:What does f(x) = x^2 describe in nature
ELorenz wrote:it states that vectors actually first appeared in geometry
The idea of a vector is one of the greatest contributions to mathematics, which came directly from physics.
ELorenz wrote:a point itself could be a vector in mathematics.
A finite dimensional vector space over R with an inner product defined on it is called an Euclidean space
ELorez wrote:are fields and vector spaces.
You might be thinking of the Euclidean metric rather than Euclidean space.
JMas wrote:ELorenz,
I think I know the point you're trying to make. Mathematics is a language that can be used to model nature, though, this is not its sole responsibility/endeavour (this is a huge topic).
As for your f(x) = x^2, well, this relation describes one of the more important natural laws. The Harmonic Potential:
U = 1/2 * k * x^2
where;
U = Harmonic Potential
k = a positive constant
x = displacement
This has been used in a lot of models, for example, an approximation of lattice vibrations in crystals (small amplitude), called the "Harmonic Limit" or "Harmonic Approximation" and the Quantum harmonic oscillator (V. Important) amongst others.
Ma77o wrote:Is math discovered, or invented?
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