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In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. [1]
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...
For example, a Fourier series of sine and cosine functions, all continuous, may converge pointwise to a discontinuous function such as a step function. Carmichael's totient function conjecture was stated as a theorem by Robert Daniel Carmichael in 1907, but in 1922 he pointed out that his proof was incomplete. As of 2016 the problem is still open.
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An example spangram with corresponding theme words: PEAR, FRUIT, BANANA, APPLE, etc. ... NYT Strands Spangram Answer Today. Today's spangram answer on Saturday, January 18, 2025, is CAPTAIN. ...
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.
The app allows you to display three Hinge prompt answers, with a myriad of options to choose from (including voice and video prompts!). These range from funny, to deep, to nerdy. The challenge is ...
From ancient history to the modern day, the clitoris has been discredited, dismissed and deleted -- and women's pleasure has often been left out of the conversation entirely. Now, an underground art movement led by artist Sophia Wallace is emerging across the globe to challenge the lies, question the myths and rewrite the rules around sex and the female body.