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| สมัครสมาชิก | คู่มือการใช้ | รายชื่อสมาชิก | ปฏิทิน | ข้อความวันนี้ | ค้นหา |
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เครื่องมือของหัวข้อ | ค้นหาในหัวข้อนี้ |
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#2
11 พฤษภาคม 2015, 10:10
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De Bruijn's theorem.
In a 1969 paper, Dutch mathematician Nicolaas Govert de Bruijn proved several results about packing congruent rectangular bricks (of any dimension) into larger rectangular boxes, in such a way that no space is left over. One of these results is now known as de Bruijn's theorem. According to this theorem, a "harmonic brick" (one in which each side length is a multiple of the next smaller side length) can only be packed into a box whose dimensions are multiples of the brick's dimensions.[1] 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.[1] This theorem was first published by Joseph-Émile Barbier in 1860.[2] The most familiar examples of curves of constant width are the circle and the Reuleaux triangle. For a circle, the width is the same as the diameter; a circle of width w has perimeter πw. A Reuleaux triangle of width w consists of three arcs of circles of radius w. Each of these arcs has central angle π/3, so the perimeter of the Reuleaux triangle of width w is equal to half the perimeter of a circle of radius w and therefore is equal to πw. A similar analysis of other simple examples such as Reuleaux polygons gives the same answer. 
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#3
11 พฤษภาคม 2015, 10:15
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Carnot's theorem
In Euclidean geometry, Carnot's theorem states that the sum of the signed distances from the circumcenter D to the sides of an arbitrary triangle ABC is DF + DG + DH = R + r,\ where r is the inradius and R is the circumradius of the triangle. Here the sign of the distances is taken negative if and only if the line segment DX (X = F, G, H) lies completely outside the triangle. In the picture DF is negative and both DG and DH are positive. The theorem is named after Lazare Carnot (1753?1823). It is used in a proof of the Japanese theorem for concyclic polygons. De Gua's theorem De Gua's theorem is a three-dimensional analog of the Pythagorean theorem and named for Jean Paul de Gua de Malves. If a tetrahedron has a right-angle corner (like the corner of a cube), then the square of the area of the face opposite the right-angle corner is the sum of the squares of the areas of the other three faces. A_{ABC}^2 = A_{\color {blue} ABO}^2+A_{\color {green} ACO}^2+A_{\color {red} BCO}^2
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#7
11 พฤษภาคม 2015, 17:34
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ใช่เลยครับ ดูรายละเอียดที่
Heron's formula ที่น่าสนใจคือ หัวข้อ Numerical stability Heron's formula as given above is numerically unstable for triangles with a very small angle when using floating point arithmetic. A stable alternative [8] [9] involves arranging the lengths of the sides so that a >= b >= c and computing ตามสูตรปรับปรุง
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#8
11 พฤษภาคม 2015, 17:39
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ทฤษฎีของ Brahmagupta
ดู Heron's formula ในหัวข้อ Generalizations Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the quadrilateral to zero. Heron's formula is also a special case of the formula for the area of a trapezoid or trapezium based only on its sides. Heron's formula is obtained by setting the smaller parallel side to zero. Expressing Heron's formula with a Cayley?Menger determinant in terms of the squares of the distances between the three given vertices, illustrates its similarity to Tartaglia's formula for the volume of a three-simplex. Another generalization of Heron's formula to pentagons and hexagons inscribed in a circle was discovered by David P. Robbins.[13]
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