curves of constant width造句

• It is therefore a curve of constant width.
• There is also the concept of space curves of constant width, whose widths are defined by tangent planes.
• In case the noodle is any closed curve of constant width D the number of crossings is also exactly 2.
• These two facts can be combined to give a short proof of Barbier's theorem on the perimeter of curves of constant width.
• The first mathematician to discover the existence of curves of constant width, and to observe that the Reuleaux triangle has constant width, may have been Leonhard Euler.
• The Reuleaux triangle is the first of a sequence of "'Reuleaux polygons "', curves of constant width formed from regular polygons with an odd number of sides.
• A basic result on curves of constant width is Barbier's theorem, which asserts that the perimeter of any curve of constant width is equal to the width ( diameter ) multiplied by ?.
• A basic result on curves of constant width is Barbier's theorem, which asserts that the perimeter of any curve of constant width is equal to the width ( diameter ) multiplied by ?.
• Additionally, if " K " is ( the interior of ) a curve of constant width, then the Minkowski sum of " K " and of its 180?rotation is a disk.
• Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides ( triangle, pentagon, heptagon, etc . ).
• In a paper that he presented in 1771 and published in 1781 entitled " De curvis triangularibus ", Euler studied curvilinear triangles as well as the curves of constant width, which he called orbiforms.
• The reason why until now the geometry of curves of constant width could not be put to practical use in the gear design is that no conventional gear structure with the regular rolling on of the gears would permit the exact rolling-on of the singularities.
• :: : The loonie has 11 sides and not, say, 10 or 12 because its shape is a curve of constant width ( like a Reuleaux triangle or the 7-sided British coins ) and therefore the number of sides must be odd.
• Curves of constant width are also the general answer to a brain teaser : " What shape can you make a manhole cover so that it cannot fall down through the hole ? " In practice, there is no compelling reason to make manhole covers non-circular.
• If the width of D is the same in all directions, the body is said to have " constant width " and its boundary is a " curve of constant width "; the planar body itself is called an " orbiform ".
• There exists a polynomial f ( x, y ) of degree 8, whose graph ( i . e ., set of points in \ R ^ 2 for which f ( x, y ) = 0 ) is a non-circular curve of constant width.
• :: : Found the Wikipedia article : Curve of constant width ( I didn't find it before because it didn't contain the string " roll " at all, until I added something just now . . . ) talk ) 08 : 03, 28 November 2010 ( UTC)
• In each rotor of the Wankel engine, the oval-like epitrochoid-shaped housing surrounds a rotor which is triangular with bow-shaped flanks ( often confused with a Reuleaux triangle, a three-pointed curve of constant width, but with the bulge in the middle of each side a bit more flattened ).
• In geometry, a "'curve of constant width "'is a convex planar shape whose width ( defined as the perpendicular distance between two distinct parallel lines each having at least one point in common with the shape's boundary but none with the shape's interior ) is the same regardless of the orientation of the curve.
• He showed that a cover for all curves of constant width one is also a cover for all sets of diameter one and that a cover can be constructed by taking a regular hexagon with an inscribed circle of diameter one and removing two corners from the hexagon to give a cover of area 2-\ frac { 2 } { \ sqrt { 3 } } = 0.84529946.