Cyrusrobati

dear sir/madam: greetings

i do possess a string of new equations in mathematics (already been confirmed by my university. i wonder if you could have them displayed in your site pages. thank you. sincerely yours, cyrus g. robati₡

Wikipedia error

in this site: https://en.wikipedia.org/wiki/Absolute_value it has been said that

Derivative

The real absolute value function has a derivative for every x ≠ 0, but is not differentiable at x = 0. Its derivative for x ≠ 0 is given by the step function[10][11]

correction: it is not the step function, but the correct answer should be the 'sigma' function ('sign function')₡

projectile motion

in your site at https://en.wikipedia.org/wiki/Projectile_motion it is given

Parabolic trajectory Main article: Trajectory of a projectile

Consider the equations,

   x = v_0 t \cos(\theta) ,
   y = v_0 t \sin(\theta) - \frac{1}{2}gt^2 .

If t is eliminated between these two equations the following equation is obtained:

   y=\tan(\theta) \cdot x-\frac{g}{2v^2_{0}\cos^2 \theta} \cdot x^2 ,

This equation is the equation of a parabola. Since g , \theta , and \mathbf{v}_0 are constants, the above equation is of the form

   y=ax+bx^2 ,

in which a and b are constants. This is the equation of a parabola, so the path is parabolic. The axis of the parabola is vertical.

correction:

   y=ax-bx^2 ,

(the correct equation of a parabola)

Metric signature

there is an error at https://en.wikipedia.org/wiki/Metric_signature

Signature in physics

In mathematics, the usual convention for any Riemannian manifold is to use a positive-definite metric tensor (meaning that after diagonalization, elements on the diagonal are all positive).

In theoretical physics, spacetime is modeled by a pseudo-Riemannian manifold. The signature counts how many time-like or space-like characters are in the spacetime, in the sense defined by special relativity: as used in particle physics, the metric is positive definite on the time-like subspace, and negative definite on the space-like subspace. In the specific case of the Minkowski metric,

   ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 ,

the metric signature is (1, 3, 0), since it is positive definite in the time direction, and negative definite in the three spatial directions x, y and z. (Sometimes the opposite sign convention is used, but with the one given here s directly measures proper time.)

correction: This is in fact the flat lorentz metric (special relativity) ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 , not the minkowski metric which is ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 ,

new generalisation: heron's formula

the new generalisation involves the use of a triangle's perimeter:

Using 2a + 2b/2; 2c + 2b; 2a + 2c, one can perimeter as:

p = 2a + 2b + 2c / 2 = a + b + c

then one can rewrite heron's formula in terms of this perimeter:

₡ ∆A = 1/4 √p(p-2a)(p-2b)(p-2c)

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