Philosophy Now Forum

When I first started my studies in geometry, by my own hand and not the book, I quickly started writing the equations to the figures. Very early one puts a problem before them, and they have to figure our a triangle given just the three sides. Which I did. I called that demonstration in the Delian Quest, Pythagoras Revisited.
After that, I figured out how to take the sine of any line in any triangle, meaning I quickly trashed out Trigonometry, showing it is simply a mess of obfuscation because someone did not learn basic math.

If you want to draw it, and put the math into the worksheet, you can see it for yourself, Any triangle, with simple arithmetic, you can find the sine exactly, and thus the angle, any triangle whatsoever.

Now, I have started a couple other projects, but I have to put them on hold, because, well, this whole affair with trig is not in the elements, and all we have about angles in the elements is way too simple, simple greater than less than, and no one worked the figure, and demonstrated it as I have, should make something more educational, focused on it.

all one needs to do all the math with any triangle is just the triangle itself. Everything can be easily derived.
I even did it a couple of times, where I drew the equations nd had the equations make the perpetual motion triangle, giving the sines of all the lines.

An animation, but not exactly a cartoon.
Writing equations to figures came naturally, but I do not know why. It just did, it simply made sense to me.
The figure, itself, speaks for itself.

Here is how to do the math and draw it.

Construct any triangle, then circumscribe it. The radius of the circle is now the unit, or 1. The equation to find the radius from the triangle is shown step by step in the Delian Quest. Triangle Circumscription.

Every side of that triangle is now that line divided by twice the unit. That number, take the sine of that number, and you will find it is the angle which is over that segment.

You have taken simple arithmetic, found a ratio, the sine of which is the angle which subtends that line.

The sine of each side gives the angle which subtends each side. Every side, of every triangle, which contradicts every book ever written on Trigonometry which claims it cannot be done.

A triangle has to be understood in terms of the universe of discourse, i.e. the circle which circumscribes it, the radius of which is automatically 1, for the unit of discourse for the equations. Every line is then proportional to that unit.

People pay lip service to the tools, straightedge and compass, when the intelligible is unit and universe of discourse. That is how you pair arithmetic and algebra to the geometric figure.

So, trigonometry turns out to be a fraud perpetrated by simple lack of comprehension.

You can actually use this, using algebra, to prove what 1, is in a geometric figure.

pick any triangle in a figure, and establish the unit in accordance with the three points chosen. You will then establish that every line in a geometric figure is expressible in terms of this unit.

Once one understands this, what would things look like if this was used in physics? Every thing, in the physical matrix, expressible in terms of a common unit. Not in terms of an arbitrary unit, but one established by that which one is processing itself?

Now, that I have shown everyone who has ever viewed my work, how to do what has been traditionally claimed impossible, you might start to figure out why nobody talks about me. How would you react, to finding out, you were teaching, and preaching, gibberish? My work has been downloaded around the world, yet nobody says a word. It would upset education globally.

Still, I will press on. Leave the mess to those who created it.

Where did it all go wrong in history?

Well, it did not. Trig is older, more primitive than the Pythagorean Theorem. What happened there is nobody remembered an important process. When we reduce a thing to a particular example, we are suppose to work on generalizing it; a process never done.
When I started my self taught geometry, I realized that in order to solve a plate I wrote for myself to solve, that I would have to generalize the Pythagorean Theorem for every triangle, and that is what I did.

From that point, I eventually realized, I could solve the rest.

In short, it was just a long and drawn out evolution in history. It simply took what it took. Had Pythagoras been generalized two thousand years ago, there would be no trigonometry today.

However, there is an inverse relationship involved; the longer it takes to do what should have been done, the more mythology evolves and become canonized in the minds of man. That is why we have all these fucked up bull shit stories in science and math today.

Stupidity grows in the vacuum of intelligence.

In this round of demonstrations, I am going to evolve the method of presentation. I will present the polished traditional method I developed, but then I am going to make the presentation exactly the same, but change the naming convention by using the verb, along with having carried the original definition of it, no mater where it becomes placed in the figure, what that will do is make it not only easier to follow graphically, but also comprehend the equations easier. Or so I believe.

In short, data grouping will be more efficient.