Category: Theorems in plane geometry

Fenchel's theorem
In differential geometry, Fenchel's theorem is an inequality on the total absolute curvature of a closed smooth space curve, stating that it is always at least . Equivalently, the average curvature is
Bézout's theorem
Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of
Hjelmslev's theorem
In geometry, Hjelmslev's theorem, named after Johannes Hjelmslev, is the statement that if points P, Q, R... on a line are isometrically mapped to points P´, Q´, R´... of another line in the same plan
Intercept theorem
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 t
Mukhopadhyaya theorem
In geometry Mukhopadhyaya's theorem may refer to one of several closely related theorems about the number of vertices of a curve due to Mukhopadhyaya. One version, called the four-vertex theorem, stat
Poncelet–Steiner theorem
In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions impose
Crossbar theorem
In geometry, the crossbar theorem states that if ray AD is between ray AC and ray AB, then ray AD intersects line segment BC. This result is one of the deeper results in axiomatic plane geometry. It i
Midpoint theorem (conics)
In geometry, the midpoint theorem describes a property of parallel chords in a conic. It states that the midpoints of parallel chords in a conic are located on a common line. The common line (segment)
Pasch's theorem
In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from Euclid's postulates.
Barbier's theorem
In geometry, Barbier's theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape. This theorem was first published by Joseph-Émile Barbier in 1
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose
Blaschke–Lebesgue theorem
In plane geometry the Blaschke–Lebesgue theorem states that the Reuleaux triangle has the least area of all curves of given constant width. In the form that every curve of a given width has area at le
Holditch's theorem
In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point on the chord a distance p from one end and a d
Zone theorem
In geometry, the zone theorem is a result that establishes the complexity of the zone of a line in an arrangement of lines.
Newton's theorem about ovals
In mathematics, Newton's theorem about ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant. Isaac Newton stated it as lemma 28 of section
Mohr–Mascheroni theorem
In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that b