congruent triangles sebarhâ-ye damsâz Fr.: triangles congrus 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. |
equilateral triangle sebar-e sé-pahlu-barâbar (#) Fr.: triangle équilatéral A triangle having three equal sides. → equi-, → lateral, → triangle. Sé-pahlu-barâbar, from sé, → three, pahlu, → side, barâbar, → equal. |
isosceles triangle sebar-e do-pahlu-barâbar (#) Fr.: triangle équilatéral 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. |
Pascal's triangle sebar-e Pascal Fr.: triangle de Pascal 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. |
Reuleaux triangle sebar-e Reuleaux Fr.: triangle de Reuleaux 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. |
right triangle sebar-e râst (#) Fr.: triangle droit A triangle one of whose angles is a → right angle. |
scalene triangle sebar-e nâjur-pahlu Fr.: triangle scalène 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"). |
spherical triangle sebar-e kore-yi Fr.: triangle sphérique 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. |
summer triangle sebar-e tâbestâni Fr.: triangle d'été 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. |
triangle sebar (#), seguš (#) Fr.: 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. Sebar "three-sided," from sé, → three, +
+ bar "side; breadth; breast,"
variant var (Mid.Pers. var "breast;"
Av. vouru "wide, broad, extended" (vourucašāni- "looking far"),
related to varah- "breast;" cf. Skt. urú- "wide, broad,"
úras- "breast;" Gk. eurus "wide, broad;"
PIE base uer-, ueru-s"wide, broad"). |
triangle inequality nâhamugi-ye sebari Fr.: inégalité triangulaire 1) A theorem according to which any side of a triangle is always shorter than the sum of the
other two sides. → triangle; → inequality. |