We investigate here the representability of integers as sums of triangular numbers, where the n-th triangular number is given by Tn = n(n+1)/2. In particular, we show ...

Pythagoras’ theorem is a statement that is true for all right-angled triangles.It states that the area of the square on the hypotenuse close hypotenuseThe longest side of a right-angled triangle, ...

The textbook uses examples from Indian monuments and cultural contexts to explain key concepts of the subject, including ...

In this triangle \(a^2 = b^2 + c^2\) and angle \(A\) is a right angle. Pythagoras' theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not.

On November 26, 1949, Albert Einstein published an essay in the Saturday Review of Literature in which he described two pivotal moments in his childhood. The first involved a compass that his father ...

The most important theorem we learnt in childhood carries the name of a Greek philosopher, but not necessarily the legacy.

Do you think there’s a triangle whose angles measure 41, 76 and 63 degrees? At first, answering this may seem easy. From geometry class we know that the sum of the measures of the interior angles of a ...

This is a preview. Log in through your library . Journal Information The Mathematical Gazette is the original journal of the Mathematical Association and it is now over a century old. Its readership ...

In a new peer-reviewed study, Ne'Kiya Jackson and Calcea Johnson outlined 10 ways to solve the Pythagorean theorem using trigonometry, including a proof they discovered in high school. When you ...

Many prominent phenomena originate from geometrical effects rather than from local physics. For example, the 'hairy ball' (HB) theorem asserts that a hairy sphere cannot be combed without introducing ...