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The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...
Azuma's inequality; Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount
The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle. In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.
YouTube TV announced Thursday that the price of its subscription service will be rising, again.. In an email to customers, YouTube TV announced that it will be increasing its prices by $10 ...
“Inside Out 2” tackles this head-on. The movie’s first lesson is simple yet profound: anxiety may not feel good, but it often is good for us. Early in the film, Riley goofs around in the ...
Winter is hitting the Gaza Strip and many of the nearly 2 million Palestinians displaced by the devastating 14-month war with Israel are struggling to protect themselves from the wind, cold and rain.
The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...
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related to: hinge theorem examples with answers worksheet 2It’s an amazing resource for teachers & homeschoolers - Teaching Mama