Why is the Pythagorean theorem still called a theorem?

Slight difference between a theory and a theorem.

A theorem MUST be proven (otherwise it is a conjecture).

A theorem is only true if prior axioms are accepted. In the case of this one, the important axiom is that you are working on a "plane" (a flat 2-dimension surface with no curvature).

The equivalent axiom is the one by which two parallel lines never meet.

If you remove this axiom, then the theorem is no longer valid.

For example, on Earth's surface, draw the following triangle:

(for this exercise, we consider Earth to be a sphere)

Start at the North pole and go straight south for 10,000 km. You are at the equator. Turn 90 degrees towards the left. Go straight for 10,000 km along the equator. Turn left 90 degrees (now facing north) go back to the start point (third side = 10,000 km)

You now have an equilateral triangle (three sides of 10,000 km). Which angle is 90 degrees? ALL THREE of them.

Obviously, by the theorem, the side opposite the 90 degree angle (hypotenuse) should be longer than the other two.

in this case, each side must be longer than the other two (obviously impossible).

Therefore, when we remove the flatness axiom, the theorem is no longer valid.

Main Entry: the·o·rem

Pronunciation: \ˈthē-ə-rəm, ˈthir-əm\

Function: noun

Etymology: Late Latin theorema, from Greek theōrēma, from theōrein to look at, from theōros spectator, from thea act of seeing — more at theater

Date: 1551

1 : a formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions

therefore, a Theorem, like the Pythagorean Theorem, is deduced from other formulas or propositions

you state Pythagora is a destructive guy, yet what could you tell to the genuine person who invented it? i studied it replaced into no longer Pythagora to truly understand this theorem or regulation as you call it

Theorem doesn't mean it is only proven by one method. Theorem just means that has been proven true.