L-moment: Difference between revisions

Revision as of 21:59, 31 July 2013

A trammel of Archimedes is a mechanism that traces out an ellipse.^[1] It consists of two shuttles which are confined ("trammelled") to perpendicular channels or rails, and a rod which is attached to the shuttles by pivots at fixed positions along the rod. As the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path. The semi-axes a and b of the ellipse are the distances between the end of the rod and the two pivots. An ellipsograph is a trammel of Archimedes intended to draw, cut, or machine ellipses, e.g. in wood or other sheet materials. An ellipsograph has the appropriate instrument (pencil, knife, router, etc.) attached to the rod. Usually the distances a and b are adjustable, so that the size and shape of the ellipse can be varied.

The history of such ellipsographs is not certain, but they are believed to date back to Proclus and perhaps even to the time of Archimedes.^[2]

An animation of a Trammel of Archimedes in action.

Wooden versions of the trammel of Archimedes have been produced also as toys or novelty items, and sold under the name of nothing grinders or do nothing machines. In these toys the drafting instrument is replaced by a crank handle, and the position of the sliding shuttles is usually fixed.

Mathematics

Let C be the end of the rod, and A, B be the pivots of the sliders. Let p and q be the distances from A to B and B to C, respectively. Let us assume that sliders A and B move along the y and x coordinate axes, respectively. When the rod makes an angle θ with the x-axis, the coordinates of point C are given by

x=(p+q)\cos \theta \,

y=q\sin \theta \,

These are in the form of the standard parametric equations for an ellipse in canonical position. The further equation

{\frac {x^{2}}{(p+q)^{2}}}+{\frac {y^{2}}{q^{2}}}=1

is immediate as well.

The trammel of Archimedes is a special case of the more general oblique trammel. The axes constraining the pivots do not have to be perpendicular and the points A, B and C can form a triangle. The resulting locus of C is still an ellipse.^[2]

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

J. W. Downs: Practical Conic Sections: The Geometric Properties of Ellipses, Parabolas and Hyperbolas. Courier Dover 2003, ISBN 978-0-486-42876-5, pp. 4–5 (Template:Google books)

External links

Cutting ellipses in wood
Photo of a Kentucky Do-Nothing
Instructions on how to build a Kentucky Do-Nothing
Video of a Do-Nothing made from Lego bricks
"Wonky Trammel of Archimedes" An exploration of a generalized trammel.
Patent for ellipse cutting guide allowing small ellipses

↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 (Template:Google books)
↑ ^2.0 ^2.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[1] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 (Template:Google books)

[AMM-2] 2.0 ^2.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[1]

[2]

@@ Line 1: / Line 1: @@
+[[File:Archimedes Trammel.gif|right|thumb|Trammel of Archimedes.]]
+A '''trammel of Archimedes''' is a mechanism that traces out an [[ellipse]].<ref>{{cite book |title=The Words of Mathematics |last=Schwartzman |first=Steven |year=1996 |publisher=The [[Mathematical Association of America]] |isbn=0-88385-511-9}} ({{Google books|SRw4PevE4zUC|restricted online copy|page=223}})</ref> It consists of two shuttles which are confined ("[[Wikt:trammel|trammelled]]") to perpendicular channels or rails, and a rod which is attached to the shuttles by pivots at fixed positions along the rod. As the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path.  The semi-axes ''a'' and ''b'' of the ellipse are the distances between the end of the rod and the two pivots.
+An '''ellipsograph''' is a trammel of Archimedes intended to draw, cut, or machine ellipses, e.g. in [[wood]] or other sheet materials.  An ellipsograph has the appropriate instrument (pencil, knife, [[wood router|router]], etc.) attached to the rod.  Usually the distances ''a'' and ''b'' are adjustable, so that the size and shape of the ellipse can be varied.
+The history of such ellipsographs is not certain, but they are believed to date back to [[Proclus]] and perhaps even to the time of [[Archimedes]].<ref name=AMM/>
-Companies know that investing in your workforce will have immeasurable impact [http://tinyurl.com/ku6vjks uggs on sale] the bottom-line but not  [http://tinyurl.com/ku6vjks ugg boots] too many will even consider allowing one of its employees to pursue a Master of Business Administration, much less pay for the continuing education. Unfortunately, companies balk at the sacrifice involved.<br>It takes a lot to adjust all your operations to cater to a single employee who might have to sacrifice some of his or her responsibilities to focus [http://tinyurl.com/ku6vjks uggs on sale] the studies.<br><br>Developing human resource<br>Developing your workforce-through retraining and education-and aligning those with your overall business mission will ensure mid-term and long-term gains. What holds back most companies in supporting an employee get a Master of Business Administration degree is the fear that the worker will leave afterwards.<br>The studies, however, say otherwise. <br><br>A Louis Harris and Associates survey in 2010 revealed that employees are more likely to leave the company that offers no training opportunities. According to the survey, 4 in 10 of those employees were planning to find better opportunities elsewhere within the year.<br>[http://tinyurl.com/ku6vjks uggs on sale] the flip side, only about 12 percent of the employees who worked for companies that offer continuing education and training said they will be leaving. So to say that investing in education of your employees will prompt them to leave doesn't really hold water.<br><br>Benefits <br>The Louis Harris and Associates survey was further buttressed by the National Network of Sector Partners which stated that developing human resource will boost company bottom-line. Among the benefits to the employer who allows its employees to pursue a Master of  [http://tinyurl.com/ku6vjks ugg boots sale] Business Administration degree include taking advantage of any innovation or new updates in the industry, it can reduce employee turnover as the employees are more likely to stay, boost productivity and improve work [http://Wordpress.org/search/quality quality].<br><br>What should companies do?<br>Clearly, companies need to rethink their perception of the value of education and how it will help them become more competitive. The company can  [http://tinyurl.com/ku6vjks ugg boots] invest in tuition assistance programs to encourage employees-whose budgets are already strained by the [http://data.Gov.uk/data/search?q=economic+slowdown-into economic slowdown-into] taking a Master of Business Administration degree.<br>Aside from debt of gratitude for helping pay off the school fees, the opportunity of career advance will prevent employees from leaving. The company should also accommodate the employee's harder schedule as she or she juggles work, family and schooling by allowing time off as long as necessary.<br><br>This will ensure that the company will get back its investment by making it easier for the employee to get his or her degree in Master of Business Administration.
+[[File:Trammel of Archimedes Small White.gif|right|thumb|An animation of a Trammel of Archimedes in action.]]
+Wooden versions of the trammel of Archimedes have been produced also as [[toy]]s or [[novelty item]]s, and sold under the name of '''nothing grinders''' or '''do nothing machines'''.  In these toys  the drafting instrument is replaced by a [[Crank (mechanism)|crank]] handle, and the position of the sliding shuttles is usually fixed.
+== Mathematics ==
+[[File:Archimedes Trammel Diagram.png|thumb|Diagram]]
+Let ''C'' be the end of the rod, and ''A'', ''B'' be the pivots of the sliders.  Let ''p'' and ''q'' be the distances from ''A'' to ''B'' and ''B'' to ''C'', respectively.  Let us assume that sliders ''A'' and ''B'' move along the ''y'' and ''x'' [[Cartesian coordinates|coordinate]] axes, respectively.  When the rod makes an angle ''θ'' with the ''x''-axis, the coordinates of point ''C'' are given by
+:<math>x = (p+q) \cos\theta\,</math>
+:<math>y = q \sin\theta\,</math>
+These are in the form of the standard parametric equations for an ellipse in canonical position. The further equation
+:<math>\frac{x^2}{(p+q)^2}+ \frac{y^2}{q^2}= 1</math>
+is immediate as well.
+The trammel of Archimedes is a special case of the more general oblique trammel. The axes constraining the pivots do not have to be perpendicular and the points ''A'', ''B'' and ''C'' can form a triangle. The resulting locus of ''C'' is still an ellipse.<ref name=AMM>{{cite journal|last=Wetzel|first=John E.|title=An Ancient Elliptic Locus|journal=[[American Mathematical Monthly]]|date=February 2010|volume=117|issue=2|pages=161–167|jstor=10}}</ref>
+==See also==
+* [[Beam compass]]
+* [[Useless machine]]
+==Notes==
+{{reflist}}
+==References==
+* J. W. Downs: ''Practical Conic Sections: The Geometric Properties of Ellipses, Parabolas and Hyperbolas''. Courier Dover 2003, ISBN 978-0-486-42876-5, pp.&nbsp;4–5 ({{Google books|pHxTQTiYkGYC|restricted online copy|page=4}})
+==External links==
+*[http://www.woodweb.com/knowledge_base/A_Jig_for_Drawing_or_Cutting_Ellipses.html Cutting ellipses in wood]
+*[http://www.flickr.com/photos/sakraft1/3375895909/ Photo of a Kentucky Do-Nothing]
+*[http://www.instructables.com/id/Do_nothing_Machine/ Instructions] on how to build a Kentucky Do-Nothing
+*[http://www.youtube.com/watch?v=GzQfQa8uv6M Video] of a Do-Nothing made from [[Lego]] bricks
+*[http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/WonkyTrammel.pdf "Wonky Trammel of Archimedes"] An exploration of a generalized trammel.
+*[http://www.freepatentsonline.com/4306598.html Patent for ellipse cutting guide allowing small ellipses]
+[[Category:Traditional toys]]
+[[Category:Mechanisms]]
+[[Category:Conic sections]]
+[[Category:Novelty items]]

L-moment: Difference between revisions

Revision as of 21:59, 31 July 2013

Contents

Mathematics

See also

Notes

References

External links

Navigation menu

L-moment: Difference between revisions

Revision as of 21:59, 31 July 2013

Mathematics

See also

Notes

References

External links

Navigation menu

Search