User:Ricardo sandoval

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My main interest is in math articles.

Main contributions

Trigonometric functions: One paragraph near the end talking about the harmonic motion. I was impressed no one did that before, since it is a very important physics concept. Also pointed trigonometric functions are projections of the circular movement. And explained the animation on the side.

To do: The circular movement explains the derivatives of the sine and cosine very nicely, I wonder were that could fit.

Euler's formula: A demonstration of the Euler formula in the section differential equations proof (e^{ix}'=ie^{ix}). I think this demonstration is more direct and intuitive. Observation at the beginning of proofs, since problems with rigor as definition of the e^{ix} used is not cited in some proofs, I fixed it partially. Added a definition by limit of e^{z} as lim(1+z/n)^n.

To do: Too many proofs in the Euler's formula maybe a new page should be made. Don't know what to make of some of the proofs.

Thales theorem: Added a geometrical proof of the converse, I think it makes the converse more intuitive.

To do: Add a picture showing the rectangle and the half right triangle.

Minor changes

Golden ratio: Tried a more clear wording for the lead and calculation parts.

Sine law: Added 2R = \frac{abc} {2A} to make the equation more understandable and useful.

Pythagorean theorem: Added the "If the angle between the sides is right it reduces to the Pythagorean theorem" to make the citation of the cosine law more understandable.

Heron's formula: Completed the steps on the demonstration using difference of squares.

Pi: Added that the ratio c/d is always the same so the definition makes sense.

Rectangle: Added that the diagonal crosses at he midpoints, are equal, amd can be calculated using Pythagoras.

Complex numbers: Added a link to Visual complex Analysis a book by Tristan Needham.