Starship Asterisk*

I never met a weapon i did'nt like Ronald Regan ( 1989 )

http://en.wikipedia.org/wiki/Reuleaux_triangle wrote:
The Reuleaux triangle is a constant width curve based on an equilateral triangle.

All points on a side are equidistant from the opposite vertex.

A Reuleaux triangle is, apart from the trivial case of the circle, the simplest and best known Reuleaux polygon, a curve of constant width. The separation of two parallel lines tangent to the curve is independent of their orientation. The term derives from the name of Franz Reuleaux, a 19th-century German engineer who did pioneering work on ways that machines translate one type of motion into another, although the concept was known before his time.

The Reuleaux triangle has the least area of any curve of given constant width. The Reuleaux triangle can be generalized to regular polygons with an odd number of sides, yielding a Reuleaux polygon. The most commonly used of these is the Reuleaux heptagon. The British twenty pence and fifty pence coins are approximately Reuleaux heptagons with rounded apices, the constant width allows use in coin-operated machines.

* Because all diameters are the same length, the Reuleaux triangle, with all other Reuleaux polygons, is an answer to the question "Other than a circle, what shape can you make a manhole cover so that it cannot fall down through the hole?"

* The rotor of the Wankel engine is easily mistaken for a Reuleaux triangle but its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width.

* A drill bit in the shape of a Reuleaux triangle can, if mounted in a special chuck which allows for the bit not having a fixed centre of rotation, drill a hole that is very nearly a perfect square. Other Reuleaux polygons are used for drill bits for pentagonal, hexagonal, and octagonal holes.

* A Reuleaux triangle can roll but makes a poor wheel because it does not roll about a fixed center of rotation. An object on top of rollers with cross-sections that were Reuleaux triangles would roll smoothly and flatly, but an axle attached to Reuleaux triangle wheels would bounce up and down three times per revolution. This concept was used in a science fiction short story by Poul Anderson titled "The Three-Cornered Wheel."

* Several pencils are manufactured in this shape, rather than the more traditional round or hexagonal barrels. They are usually promoted as being more comfortable or encouraging proper grip, as well as being less likely to roll off tables.

* The shape is used for signage for the National Trails System administered by the United States National Park Service[4], as well as the logo of Colorado School of Mines.

* The Reulaux triangle is used as the rear wheel for the multi-angle-wheel bicycle built in Qingdao of Shandong Province, China.>>

http://en.wikipedia.org/wiki/Reuleaux_tetrahedron#Meissner_bodies wrote:
<<The Reuleaux tetrahedron is the intersection of four spheres of radius s centered at the vertices of a regular tetrahedron with side length s. The sphere through each vertex passes through the other three vertices, which also form vertices of the Reuleaux tetrahedron. The Reuleaux tetrahedron has the same face structure as a regular tetrahedron, but with curved faces: four vertices, and four curved faces, connected by six circular-arc edges.

This shape is defined and named by analogy to the Reuleaux triangle, a two-dimensional curve of constant width. One can find repeated claims in the mathematical literature that the Reuleaux tetrahedron is analogously a surface of constant width, but it is not true: the two midpoints of opposite edge arcs are separated by a larger distance,

Meißner & Schiller (1912) showed how to modify the Reuleaux tetrahedron to form a surface of constant width, by replacing three of its edge arcs by curved patches formed as the surfaces of rotation of a circular arc. According to which three edge arcs are replaced (three that have a common vertex or three that form a triangle) there result two noncongruent shapes that are sometimes called Meissner bodies or Meissner tetrahedra (pictures and films in Weber 2009). Bonnesen & Fenchel (1934) conjectured that Meissner tetrahedra are the minimum-volume three-dimensional shapes of constant width, a conjecture which is still open. In connection with this problem, Campi, Colesanti & Gronchi (1996) showed that the minimum volume surface of revolution with constant width is the surface of revolution of a Reuleaux triangle through one of its symmetry axes.>>

beyond wrote:Reminds me of the Wankel Rotary engine.

neufer wrote:

http://en.wikipedia.org/wiki/Reuleaux_triangle wrote:

• The rotor of the Wankel engine is easily mistaken for a Reuleaux triangle but its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width.

swainy wrote:Good job, The Roman's never realized most of their, Answers to their impossible questions was "Round" . Do you think the impossible answers to "Our" Impossible questions Might be Round?

tc

beyond wrote:With all this talk of "round", we'd better circle the wagons before the squares and triangles and all the other shapes start attacking to get us to mention them also.

http://en.wikipedia.org/wiki/Flatland wrote:
<<Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as "a square", Abbott used the fictional two-dimensional world of Flatland to offer pointed observations on the social hierarchy of Victorian culture.

Men are portrayed as polygons whose social class is directly proportional to the number of sides they have; therefore, triangles, having only three sides, are at the bottom of the social ladder and are considered generally unintelligent, while the Priests are composed of multi-sided polygons whose shapes approximate a circle, which is considered to be the "perfect" shape. On the other hand, females consist only of lines and are required by law to sway back and forth and sound a "peace-cry" as they walk, because when a line is coming towards an observer in a 2-D world, their body appears merely as a point. The Square talks of accounts where men have been killed (both by accident and on purpose) by being stabbed by women. This explains the need for separate doors for women and men in buildings. Also, colors in Flatland were banned when lower classes painted themselves to appear to be higher ordered.

In the world of Flatland, classes are distinguished using the "Art of Hearing", the "Art of Feeling" and the "Art of Sight Recognition". Classes can be distinguished by the sound of one's voice, but the lower classes have more developed vocal organs, enabling them to feign the voice of a polygon or even a circle. Feeling, practised by the lower classes and women, determines the configuration of a person by feeling one of their angles. The "Art of Sight Recognition", practised by the upper classes, is aided by "Fog", which allows an observer to determine the depth of an object. With this, polygons with sharp angles relative to the observer will fade out more rapidly than polygons with more gradual angles. The population of Flatland can "evolve" through the Law of Nature, which states: "a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on."

This rule is not the case when dealing with isosceles triangles (Soldiers and Workmen), for their evolution occurs through eventually achieving the status of an equilateral triangle, removing them from serfdom. The smallest angle of an isosceles triangle gains thirty arcminutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons; the sons of several hundred-sided polygons will often develop fifty or more sides more than their parents.

The isosceles triangles with the smallest angle are the soldier class (if they weren't criminals), while the triangles closer to being regular are menial laborers. An equilateral Triangle is a member of the craftsman class. Squares and Pentagons are the "gentlemen" class, as doctors, lawyers, and other professions. Hexagons are the lowest rank of nobility, all the way up to (near) circles, who make up the priest class. The higher order polygons have much less of a chance of producing sons, preventing flatland from being overcrowded with noblemen.

Regular polygons were considered in isolation until chapter 7 of the book when the issue of irregularity, or physical deformity, became considered. In a two dimensional world a regular polygon can be identified by a single angle and/or vertex. In order to maintain social cohesion, irregularity is to be abhorred, with moral irregularity and criminality cited, "by some" (in the book), as inevitable additional deformities, a sentiment concurred by the author. If the error of deviation is above a stated amount the irregular faces euthanasia; if below, he becomes the lowest rank of civil servant. In this study of what was to later to become known as eugenics, an irregular polygon should not be destroyed at birth, but rather allowed to develop in order to see if its irregularity could be “cured” or reduced to within society's level of tolerance. If the deformity could not be corrected then the irregular should be “painlessly and mercifully consumed.”>>

THX1138 wrote:I fricken love this site, all of you crack me up constantly, how about you makc, where you at with your reply to this thread we got going round here?

THX1138 wrote:Indeed, My personal round favorite / The beach boys. Round, round get around I get around

THX1138 wrote:I fricken love this site, all of you crack me up constantly, how about you makc, where you at with your reply to this thread we got going round here?
Astronomy picture of the day #1
Physorg.com #2
Cant tell you #3 but I’m certain you could guess

Good day all, headed to the beach to catch some waves

I never met a weapon I didnt like Ronald Regan ( 1989 )