Ancient Greek mathematics

relation in Euclidean geometry among the three sides of a right triangle

thumb|Bi-quinary coded decimal-like abacus representing

ratio between two quantities whose sum is at the same ratio to the larger one

curve obtained by intersecting a cone and a plane

formula for calculating the area of a triangle

ancient analog computer designed to calculate astronomical positions

geometric problem

numeration system used by the Koine Greek and earlier

spiral with constant width between its turnings; in polar coordinates, distance from the origin is linearly proportional to angle

theorem

axiom in Euclidean geometry

theorem

theorem

geometry of the two-dimensional surface of a sphere

way of drawing geometric objects using only an idealized compass and straightedge

geometric problem of constructing a cube with twice the volume of a given cube

construction of an angle equal to one third a given angle

mathematics texts and advances written in Greek

In the context of numeric naming systems for powers of ten, myriad is the quantity ten thousand (10,000). Idiomatically, in English, myriad is an adjective used to mean that a group of things has indefinitely large quantity.

primitive way of calculating area

construct circles that are tangent to three given circles in a plane

geometric location

shape bounded by arcs of two circles whose area is a rational multiple of the circles' radii

theorem that, if the vertices of a hexagon lie alternately on two lines, then the three pairs of opposite sides meet in three collinear points

theorem that, for a solid of revolution of a planar figure, the surface area equals the figure’s perimeter times the distance the perimeter’s centroid travels, and the volume equals the figure’s area times the distance the figure’s centroid travels

geometric construction used in Ancient Greek mathematics

a family of circles where every one intersects every circle in a second family of circles orthogonally

mathematical term in the context of differential equations

thumb|200px| The tetractys The tetractys (), or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.

mathematical curve

spiral composed of right triangles, placed edge-to-edge

when two functions have co-rational periods, i.e. n T1 = m T2

theorem that, in a right triangle, the altitude equals the geometric mean of the the two line segments on the hypotenuse created by the altitude

symbolic number notation used by the ancient Greeks

right|thumb|320px|An arbelos (grey region) thumb|Arbelos sculpture in Kaatsheuvel, Netherlands

classical average

two congruent circles within an arbelos, tangent to a segment perpendicular to the base

regular polygon that can be constructed with compass and straightedge

Relates areas of three parallelograms attached to three sides of an arbitrary triangle

chain of tangent circles within an arbelos

inequality relating the six distances between four points on a plane

algebraic curve

circle in the arbelos congruent to the twin circles

quartic plane curve; bicircular quartic curves that are symmetric with respect to the x and y-axes. Spiric sections are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals

table using constrained sand for modelling or educational purposes

Abacus found in Salamina

type of curve

unspecified value mentioned by Plato

2nd century CE trigonometric table

line segment defined from an angle and a point: given a point P that lies inside an angle with edges d and e, the shortest line segment that passes through P and has its endpoints on d and e