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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The tangent-secant theorem can be proven using similar triangles (see graphic). Like the intersecting chords theorem and the intersecting secants theorem, the tangent-secant theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle, namely, the power of point theorem.
Alternate Interior Angles Theorem ; Alternate segment theorem ; Angle bisector theorem (Euclidean geometry) Anne's theorem ; Apollonius's theorem (plane geometry) Barbier's theorem ; Beck's theorem (incidence geometry) Beckman–Quarles theorem (Euclidean geometry) Beer's theorem (metric geometry)
Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem.
In 1961, Jan-Erik Roos published an incorrect theorem about the vanishing of the first derived functor of the inverse limit functor under certain general conditions. [16] However, in 2002, Amnon Neeman constructed a counterexample. [17] Roos showed in 2006 that the theorem holds if one adds the assumption that the category has a set of ...
The 6th problem concerns the axiomatization of physics, a goal that 20th-century developments seem to render both more remote and less important than in Hilbert's time. Also, the 4th problem concerns the foundations of geometry, in a manner that is now generally judged to be too vague to enable a definitive answer.
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
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 polynomial. This equivalence reduces the original geometric problem to a purely algebraic problem. Every rational number is constructible.