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In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
The duplication formula and the multiplication theorem for the gamma function are the prototypical examples. The duplication formula for the gamma function is (+) = ().It is also called the Legendre duplication formula [1] or Legendre relation, in honor of Adrien-Marie Legendre.
Duplication, or doubling, multiplication by 2; Duplication matrix, a linear transformation dealing with half-vectorization; Doubling the cube, a problem in geometry also known as duplication of the cube; A type of multiplication theorem called the Legendre duplication formula or simply "duplication formula"
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
SPOILERS BELOW—do not scroll any further if you don't want the answer revealed. The New York Times. Today's Wordle Answer for #1271 on Wednesday, December 11, 2024.
Welcome to the Daily Weather Update from FOX Weather. It’s Wednesday, Dec. 11, 2024. Start your day with everything you need to know about today's weather. You can also get a quick briefing of ...
Elon Musk's government efficiency panel wants "high IQ" employees and plans weekly livestreams, according to X posts about President-elect Donald Trump's initiative to streamline the U.S. bureaucracy.
The triple-angle formula gives an expression relating the cosines of the original angle and its trisection: cos θ = 4 cos 3 θ / 3 − 3 cos θ / 3 . It follows that, given a segment that is defined to have unit length, the problem of angle trisection is equivalent to constructing a segment whose length is the root of a cubic ...
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