Perfect Equations
Posted: Sat Nov 15, 2025 1:38 am
A perfect equation is one in which contains only what is given and is always true.
For example.
Let us say you want the equation for the height and medial bisector of any triangle given only the three sides.
Now, if you can do that, you can also say what the area of any triangle is given only the sides.
Let us call each side, A, B, and C, where A is your chosen base.
The height we will call D, and the medial bisector, E.
D = Square root of ((A + B + C) X (A + B - C) X (A - B + C) X (B - A + C)) /(2 x sq rt of A squared)
E = Square root of ( 2 x b squared - a squared + 2 X c squared) / 2.
Now, if you draw it in a drawing program that you can also write the equation as given, you find you can move the points any where, and the equations are always right.
That is how you do a write up, the end results can only contain the givens. There is no, Einstein fudging by putting in a constant which gets you close.
Traditional teaching about the area of a triangle gives you base and height, you will not find the equation I came up with in any textbook I know of. but, you can see how it is derived in The Delian Quest.
When you have a perfect equation, what you see, the figure, what is said arithmetically and algebraically, you have said exactly the same thing in all four members of our Grammar Matrix.
For example.
Let us say you want the equation for the height and medial bisector of any triangle given only the three sides.
Now, if you can do that, you can also say what the area of any triangle is given only the sides.
Let us call each side, A, B, and C, where A is your chosen base.
The height we will call D, and the medial bisector, E.
D = Square root of ((A + B + C) X (A + B - C) X (A - B + C) X (B - A + C)) /(2 x sq rt of A squared)
E = Square root of ( 2 x b squared - a squared + 2 X c squared) / 2.
Now, if you draw it in a drawing program that you can also write the equation as given, you find you can move the points any where, and the equations are always right.
That is how you do a write up, the end results can only contain the givens. There is no, Einstein fudging by putting in a constant which gets you close.
Traditional teaching about the area of a triangle gives you base and height, you will not find the equation I came up with in any textbook I know of. but, you can see how it is derived in The Delian Quest.
When you have a perfect equation, what you see, the figure, what is said arithmetically and algebraically, you have said exactly the same thing in all four members of our Grammar Matrix.