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Topic: Helicoid

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	Helicoid Limited: Contact
		We endeavour to answer all your queries as soon as possible.
		Helicoid Limited (registered company number: 5990601, VAT registration number: 898 6648 34) is based in London, England.
		Helicoid was founded by Alex Young in 2005 to create excellent commercial and open source web-based software.
	helicoid.net /contact (58 words)

	Laser printing system with developable helicoid reflector - Patent 4494821
		The line scanning apparatus of claim 15 wherein the sine of the angle of the specularly reflective surface of said helicoid is equal to ##EQU5## and the tangent of the angle of the pitch of said helicoid is equal to said actual radius divided by said minimum radius.
		A specularly reflective developable helicoid is disposed for rotation about the longitudinal center axis thereof to receive incident thereto the collimated light beam in a direction generally parallel to the longitudinal center axis so as to reflect the incident beam in a direction outward of the longitudinal axis toward the photosensitive medium.
		The optical means may comprise an opaque masking sheet fixedly spaced between the helicoid and the photosensitive film wherein the opaque sheet includes a radiation transmitting slit therethrough extending parallel to the longitudinal center axis of the helicoid and centered on the reflected beam.
	www.freepatentsonline.com /4494821.html (3096 words)

	Helicoid - Wikipedia, the free encyclopedia
		Its name derives from its similarity to the helix: for every point on the helicoid there is a helix contained in the helicoid which passes through that point.
		The helicoid is also a ruled surface, meaning that it is a trace of a line.
		The helicoid and the catenoid are parts of a family of helicoid-catenoid minimal surfaces.
	en.wikipedia.org /wiki/Helicoid (223 words)

	The Helicoid with Handle(s)
		The most simple of these surfaces is the singly periodic helicoid which is invariant under a translation so that the quotient surface has genus one (compare this to Riemann's minimal surface).
		For infinite twist angle, these surfaces converge to the genus one helicoid.
		This is the first example of an infinite total curvature but finite topology embedded minimal surface.
	www.indiana.edu /~minimal/essays/helicoid/index.html (161 words)

	Six types of Ruled Surfaces
		The intersection of the helicoid with a cylinder produces a helix, which would be equivalent to the railing of a spiral staircase.
		The helicoid has a wide variety of shapes, depending on the pitch, the proximity of the lines and the points, and whether the pairs of points connected by the rulings are in fact not quite diametrically opposite.
		Hence the surface, which is called a helicoid, is transformed into itself by a screw motion of the pitch d with the line of striction as axis.
	www.faculty.fairfield.edu /jmac/rs/sixmodels.htm (1452 words)

	Surface Story: Science News Online, Dec. 17, 2005
		For centuries, the plane and the helicoid were the only known examples of infinite, unbounded minimal surfaces that don't fold back to intersect themselves.
		The only remaining subtlety is to show that this surface and the helicoid with a handle discovered in the 1990s are one and the same.
		It appeared that the new sort of helicoid could have any number of tunnels and still qualify as the same sort of minimal surface as the basic helicoid and the plane.
	www.sciencenews.org /articles/20051217/bob9.asp (2017 words)

	Helicoid Flighting - Shaftless Screw Applications
		Helicoid Flighting is a continuous one-piece helix formed from bar or cut plate on special fabrication equipment into the desired diameter and pitch to fit conveyor screw pipes or shaftless screw applications.
		Falcon’s heavy helicoid flighting in carbon steel, HSLA steels and stainless steel has been used in the fabrication of shaftless screws for over 10 years.
		Use of helicoid from Falcon Industries can reduce your flighting costs for requirements in diameters to 42", thickness to 1-1/2".
	www.falconindustries.com /helicoid_flighting.htm (122 words)

	Hillman Instrument - Gauges, Valves & Thermometers (Site not responding. Last check: )
		Developed in 1941, the distinct advantages of the Helicoid gauge were quickly realized by the United States Navy and it became a Navy standard.
		Over 100,000 Helicoid gauges were made for use in Navy fighting ships, Maritime Commission vessels, and Army locomotives during World War II.
		Helicoid Gauge Division offers such instruments as digital pressure, general service and process gauges, solid state indicating pressure switches, thermometer and thermowells and chemical seals.
	www.hillmaninstrument.com /gauges/helicoid.html (128 words)

	Getting a handle on soap
		As the name suggests a helicoid has a lot of twists, in fact there are an infinite number of them; the surface looks a bit like the ramp of an infinite storey car park.
		A helicoid can be constructed by twisting the plane infinitely many times around a line of your choice within the plane.
		For the helicoid, you can prove that the mean curvature is zero at every point — meaning that there are no unnecessary bumps or bulges.
	plus.maths.org /latestnews/sep-dec05/minimal/index.html (922 words)

	Getting a handle on minimal surfaces
		A helicoid is what results when one of the simplest shapes -- a flat plane -- is twisted an infinite number of times.
		If the helicoid is vertical, its shape resembles a spiral parking ramp.
		A detailed article about the helicoid discovered by Weber and his co-workers can be found in the Dec. 17 issue of Science News at http://www.sciencenews.org/articles/20051217/bob9.asp.
	newsinfo.iu.edu /news/page/normal/2606.html (678 words)

	Giuseppe Tinaglia
		Not only are there plenty of mathematical examples for both of these surfaces (for instance planes, helicoids and catenoids are minimal surfaces while spheres, cylinders and Delauney surfaces are non zero CMC surfaces), but they can easily be realized and observed in the real world.
		The helicoid is clearly not a graph, nonetheless, each half of the helicoid minus the vertical axis can be viewed as a graph over the universal cover of the punctured plane and this is, roughly speaking, what it means to contain a multi-valued graph.
		Using the method of successive approximations, a sequence of normal variations of the helicoid can be built which converges to a non zero CMC embedded disk containing a multi-valued graph.
	www.mathematics.jhu.edu /tinaglia/research.htm (1019 words)

	Medium Format Digest Forum: P67 Helicoid Extension Tube Field Test
		I have found the helicoid to be quite useful in macro work due to its variable offset ability.
		The biggest advantage of the helicoid is that once you have your tripod set, you probably won't have to move it unlike when you use fixed extension tubes.
		I wanted to add that the helicoid's maximum magnification (with a 105mm lens) is 0.63X as opposed to the tube set, which allows 1.07X
	www.photo.net /bboard/q-and-a-fetch-msg?msg_id=002K3I (385 words)

	» A helicoid with a handle \| Emerging Technology Trends \| ZDNet.com
		Anyway, the mathematical proof that this ‘genus one helicoid’ is a minimal surface has been published and is available from Rice University under the title "An embedded genus-one helicoid." Here is the abstract.
		This genus one helicoid is constructed as the limit of a continuous one-parameter family of screw-motion invariant minimal surfaces — also asymptotic to the helicoid — that have genus equal to one in the quotient.
		A helicoid with a handle ZDNet - For the first time in more than 200 years, a team of mathematicians from Rice, Stanford and Indiana universities has discovered a new shape of geometrical minimal shape.
	blogs.zdnet.com /emergingtech/?p=65&part=rss&tag=feed&subj=zdblog (840 words)

	Math Forum Discussions (Site not responding. Last check: )
		Recalling that a helicoid is a ruled surface swept by a line that rotates along an axis like a propeller, resulting in a surface much like the internal structure of a double spiral staircase, just without the stairs.
		But I haven't been able to establish the map between the two, even though it seems intuitively obvious that is should be possible.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/thread.jspa?threadID=1163016&messageID=3813045 (208 words)

	Definition of helicoid - Merriam-Webster Online Dictionary
		2 : having the form of a flat coil or flattened spiral snail shell>
		Find more about "helicoid" instantly with Live Search
		See a map of "helicoid" in the Visual Thesaurus
	www.m-w.com /dictionary/helicoid (49 words)

	helicoid - OneLook Dictionary Search
		Helicoid : Online Plain Text English Dictionary [home, info]
		Helicoid : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include helicoid: helicoid choroidopathy, circular helicoid, helicoid parabola, hyperbolic helicoid
	www.onelook.com /?w=helicoid (267 words)

	An embedded genus-one helicoid -- Weber et al. 102 (46): 16566 -- Proceedings of the National Academy of Sciences
		An embedded genus-one helicoid -- Weber et al.
		with a single end asymptotic to the end of the helicoid.
		genus-one helicoid is constructed as the limit of a continuous
	www.pnas.org /cgi/content/abstract/102/46/16566 (319 words)

	Helicoid
		Bugtagger really helps me keep a handle on the workload at Helicoid, and I can’t wait to share it.
		The upshot is, we’ve had almost 2000 signups in a week, which means Helipad is more popular than any other Helicoid application.
		Everyone that works for Helicoid loves macs, so I’ve been bullied into writing a mac version of Helipad.
	blog.helicoid.net /articles/category/helipad (1819 words)

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