Modern triangle geometry
In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed roughly since the beginning of the last q
Square trisection
In geometry, a square trisection is a type of dissection problem which consists of cutting a square into pieces that can be rearranged to form three identical squares.
Plastic number
In mathematics, the plastic number ρ (also known as the plastic constant, the plastic ratio, the minimal Pisot number, the platin number, Siegel's number or, in French, le nombre radiant) is a mathema
Quadrature (mathematics)
In mathematics, quadrature is a historical term which means the process of determining area. This term is still used nowadays in the context of differential equations, where "solving an equation by qu
Problem of Apollonius
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 BC – c. 190 BC) posed and solved th
Italian school of algebraic geometry
In relation to the history of mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered around
La Géométrie
La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes. In the Discourse, he presents his method for obtaining clarity on any
History of trigonometry
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics
Squaring the circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a c
Divina proportione
Divina proportione (15th century Italian for Divine proportion), later also called De divina proportione (converting the Italian title into a Latin one) is a book on mathematics written by Luca Paciol
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
John Wesley Young
John Wesley Young (17 November 1879, Columbus, Ohio – 17 February 1932, Hanover, New Hampshire) was an American mathematician who, with Oswald Veblen, introduced the axioms of projective geometry, coa
Mishnat ha-Middot
The Mishnat ha-Middot (Hebrew: מִשְׁנַת הַמִּדּוֹת, lit. 'Treatise of Measures') is the earliest known Hebrew treatise on geometry, composed of 49 mishnayot in six chapters. Scholars have dated the wo
Angle trisection
Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , wher
Doubling the cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is doubl
Supergolden ratio
In mathematics, two quantities are in the supergolden ratio if the quotient of the larger number divided by the smaller one is equal to which is the only real solution to the equation . It can also be
Egyptian geometry
Egyptian geometry refers to geometry as it was developed and used in Ancient Egypt. Their geometry was a necessary outgrowth of surveying to preserve the layout and ownership of farmland, which was fl
Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-d
Euclid's Elements
The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is
Menaechmus
Menaechmus (Greek: Μέναιχμος, 380–320 BC) was an ancient Greek mathematician, geometer and philosopher born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his friendship
René Descartes
René Descartes (/deɪˈkɑːrt/ or UK: /ˈdeɪkɑːrt/; French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely co
Tetrahedron packing
In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space. Currently, the best l
History of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern m
De prospectiva pingendi
De prospectiva pingendi (On the Perspective of Painting) is the earliest and only pre-1500 Renaissance treatise solely devoted to the subject of perspective. It was written by the Italian master Piero
Apollonius of Perga
Apollonius of Perga (Greek: Ἀπολλώνιος ὁ Περγαῖος, translit. Apollṓnios ho Pergaîos; Latin: Apollonius Pergaeus; c. 240 BCE/BC – c. 190 BCE/BC) was an Ancient Greek geometer and astronomer known for h
Bhaskara I's sine approximation formula
In mathematics, Bhaskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhaskara I (c. 6
Geometric mean theorem
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line s
Glossary of classical algebraic geometry
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geo
Surya Siddhanta
The Surya Siddhanta (IAST: Sūrya Siddhānta; lit. 'Sun Treatise') is a Sanskrit treatise in Indian astronomy dated to 505 CE, in fourteen chapters. The Surya Siddhanta describes rules to calculate the