The internal Church thesis (𝗖𝗧​) is a logical principle stating that one can associate to any function f : ℕ → ℕ a concrete ...

Recall that an indefinite integral (or antiderivative) is so called as it provides a family of solutions with a constant term. It is called indefinite as the constant \(c\) can take any real value, ...

It was previously believed that trigonometry, using sine, cosine, or tangent, to verify Pythagoras’ theorem (a2 + b2 = c2) was thought to be an ultimately cyclical argument as the former is ...

In any case, by teasing sine and cosine apart, one can find “a large collection of new proofs of the Pythagorean theorem.” ...

“Trigonometric functions are based on sine and cosine ... Jackson and Johnson’s study outlines five new ways of proving the theorem using trigonometry, and their method reveals five more ...

The ratios – sine and cosine – are determined by the ... The students managed to evade circular reasoning – essentially using the theorem to prove itself. A year later, the students ...

So fundamental is the Pythagorean Theorem (a2 + b2 = c2 ... “teased two methods apart” related to its functions, sine and cosine. Their work is a rare achievement for young mathematicians.

Sine and cosine are ratios that are defined ... researchers can discover "a large collection of new proofs of the Pythagorean theorem," the young mathematicians added. Read an excerpt from ...

Pythagoras Theorem: The Pythagoras Theorem is a fundamental principle in geometry, attributed to the ancient Greek mathematician Pythagoras. This theorem establishes a relationship between the ...