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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.
The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics , two sequences of numbers, often experimental data , are proportional or directly proportional if their corresponding elements have a constant ...
Noether's theorem (Lie groups, calculus of variations, differential invariants, physics) Noether's second theorem (calculus of variations, physics) Noether's theorem on rationality for surfaces (algebraic surfaces) Non-squeezing theorem (symplectic geometry) Norton's theorem (electrical networks) Novikov's compact leaf theorem
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Gödel's second incompleteness theorem; Goodstein's theorem; Green's theorem (to do) Green's theorem when D is a simple region; Heine–Borel theorem; Intermediate value theorem; Itô's lemma; Kőnig's lemma; Kőnig's theorem (set theory) Kőnig's theorem (graph theory) Lagrange's theorem (group theory) Lagrange's theorem (number theory ...
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...
why the increased availability of easy-to-consume snack foods has had a disproportionate effect on weight gain compared to other foods. The need to employ self control in food decision making has been recognized and incorporated into other recent economic theories of obesity
Similar triangles provide the basis for many synthetic (without the use of coordinates) proofs in Euclidean geometry. Among the elementary results that can be proved this way are: the angle bisector theorem, the geometric mean theorem, Ceva's theorem, Menelaus's theorem and the Pythagorean theorem.