An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

Two triangles when all corresponding sides and interior angles have the same measure. The triangles will have the same shape and size, but one may be a mirror image of the other.

→ congruent; → triangle.

A triangle having three equal sides.

→ equi-, → lateral, → triangle.

Sé-pahlu-barâbar, from sé, → three, pahlu, → side, barâbar, → equal.

A triangle having two sides equal.

From L.L. isosceles, from Gk. isoskeles "with equal legs; that can be divided into two equal parts," from isos "equal, identical," → iso-, + skelos "leg."

Sebar, → triangle, do-pahlu-baraabar, from do, → two, pahlu, → side, barâbar, → equal.

An array of numbers in the shape of a triangle, having a 1 at the top and also at the ends of each row. Each number is obtained by summing the two adjacent numbers to it in the preceding row. Each row is a set of → binomial coefficients. In the expansion of (x + y)ⁿ, the coefficients of x and y are given by the n-th row of Pascal's traingle.

→ pascal; → triangle.

A shape of constant width created using an equilateral triangle and three similar circles. The equilateral triangle lies in the first circle with a vertex coinciding with the center of the circle and the sides equal to the circle radius. The centers of the two other circles are located at the two other vertices. The Reuleaux triangle is the intersection of the three circles.

Named after Franz Reuleaux (1829-1905), a German engineer, specialist of analysis and design of mechines; → triangle.

A triangle one of whose angles is a → right angle.

→ right; → triangle.

A triangle no two sides of which are equal.

From L.L. scalenus, from Gk. skalenos "uneven, unequal, rough," from skallein "chop, hoe," related to skolios "crooked," from PIE base *(s)qel- "crooked, curved, bent;" → triangle.

Sebar, → triangle; nâjur-pahlu "dissimilar sides," from nâjur "dissimilar, ill-matched" + pahlu "side, flank" (Mid.Pers. pahlug "side, rib," Av. pərəsu- "rib," Ossetic fars "side, flank," cf. Skt. párśu- "rib," Lith. piršys (pl.) "horse breast").

A triangle drawn on the → surface of a → sphere. A spherical triangle, like a plane triangle, may be right, obtuse, acute, equilateral, isosceles, or scalene. The sum of the angles of a spherical triangle is greater than 180° (π) and less than 540° (3π). See also → spherical excess.

→ spherical; → triangle.

The triangular shape formed by the three bright stars → Altair, → Deneb, and → Vega on the northern hemisphere's → celestial sphere, particularly visible during the summer months.

→ summer; → triangle.

The plane figure formed by three lines intersecting in pairs at three points; a three-sided → polygon. → equilateral triangle, → isosceles triangle, → scalene triangle.

M.E., from O.Fr. triangle, from L. triangulum "triangle," from neuter of adj. triangulus "three-cornered," from tri-, → three, + angulus "corner," → angle.

Seguš "three-cornered," from sé, → three, + guš "corner, → angle."
Sebar "three-sided," from sé, → three, + bar "→ side; breadth; breast."

1) A theorem according to which any side of a triangle is always shorter than the sum of the other two sides.
2) The third requirement for a → distance function describing a → metric space.

→ triangle; → inequality.