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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 ...
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
A book review in the journal Celestial Mechanics said, "In summary, the author has succeeded in producing a mathematical synthesis of the science of dynamics. The book is well presented and beautifully translated [...] Arnold's book is pure poetry; one does not simply read it, one enjoys it." [3]
The Spherics is a supplement to the Elements, and takes its content for granted as a prerequisite. The Spherics follows the general presentation style of the Elements , with definitions followed by a list of theorems (propositions), each of which is first stated abstractly as prose, then restated with points lettered for the proof.
BERLIN (Reuters) -Three parties in the eastern German state of Thuringia joined forces on Thursday to keep the poll-topping Alternative for Germany out of power, electing as state premier a ...
3. Medications. Some medications have been associated with temporary hair loss. Most of the time hair loss related to medication is due to the drug disrupting the hair growth cycle leading to a ...
Average mortgage rates are trending higher as of Thursday, December 19, 2024, a day after the Federal Reserve announced it was lowering its benchmark interest rate by 25 basis points to a range of ...
Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.