Column vector: Difference between revisions
en>Helpful Pixie Bot m ISBNs (Build J/) |
en>Legobot m Bot: Migrating 1 langlinks to WP:Wikidata - d:q2716994 |
||
| Line 1: | Line 1: | ||
__NOTOC__ | |||
{{Infobox scientist | |||
|name = Édouard Lucas | |||
|image = Elucas 1.png | |||
|image_size = 200px | |||
|alt = | |||
|caption = | |||
|birth_date = {{Birth date|1842|4|4|df=y}} | |||
|birth_place = [[Amiens]] | |||
|death_date = {{Death date and age|1891|10|3|1842|4|4|df=y}} | |||
|death_place = [[Paris]] | |||
|nationality = {{flag|France}} | |||
|fields = [[Mathematics]] | |||
|workplaces = | |||
|alma_mater = [[École Normale Supérieure]] | |||
|doctoral_advisor = | |||
|academic_advisors = | |||
|doctoral_students = | |||
|notable_students = | |||
|known_for = [[Lucas sequence]], [[Lucas-Lehmer test]], [[Lucas prime]], [[Gauss-Lucas theorem]], [[Lucas' theorem]] | |||
|influences = | |||
|influenced = [[Derrick Henry Lehmer]] | |||
|awards = | |||
|signature = <!--(filename only)--> | |||
|signature_alt = | |||
|footnotes = | |||
}} | |||
'''François Édouard Anatole Lucas''' (4 April 1842 – 3 October 1891) was a [[France|French]] [[mathematician]]. Lucas is known for his study of the [[Fibonacci sequence]]. The related [[Lucas sequence]]s and [[Lucas number]]s are named after him. | |||
==Biography== | |||
Lucas was educated at the [[École Normale Supérieure]]. He worked in the Paris observatory and later became a professor of mathematics in Paris. In the meantime he served in the army. | |||
In 1875, Lucas posed a challenge to prove that the only solution of the [[Diophantine equation]]: | |||
:<math>\sum_{n=1}^{N} n^2 = M^2\;</math> | |||
with ''N'' > 1 is when ''N'' = 24 and ''M'' = 70. This is known as the '''cannonball problem''', since it can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building a [[square pyramid]] out of them. It was not until 1918 that a proof (using [[hyperelliptic function]]s) was found for this remarkable fact, which has relevance to the [[bosonic string theory]] in 26 dimensions.<ref>{{cite web|url=http://math.ucr.edu/home/baez/week95.html |title=week95 |publisher=Math.ucr.edu |date=1996-11-26 |accessdate=2012-01-04}}</ref> [[Elementary proof]]s have been more recently published.<ref>{{Cite journal|author=Ma, D. G. |title=An Elementary Proof of the Solutions to the Diophantine Equation <math>6y^2=x(x+1)(2x+1)</math> |journal=Sichuan Daxue Xuebao |volume=4 |pages=107–116 |year=1985}}</ref><ref>{{Cite journal|author=Anglin, W. S. |title=The Square Pyramid Puzzle|jstor=2323911 |journal=[[American Mathematical Monthly]] |volume=97 |issue=2 |pages=120–124 |year=1990 |doi=10.2307/2323911}}</ref> | |||
He devised methods for testing the [[prime number|primality]] of numbers. In 1857, at age 15, Lucas began testing the primality of 2<sup>127</sup> − 1 by hand, using Lucas Sequences. In 1876, after 19 years of testing,<ref>{{cite web|url=http://primes.utm.edu/curios/page.php?number_id=135 |title=Prime Curios!: 17014...05727 (39-digits) |publisher=Primes.utm.edu |date= |accessdate=2012-01-04}}</ref> he finally proved that 2<sup>127</sup> − 1 was prime; this would remain the largest known [[Mersenne prime]] for three-quarters of a century. This may stand forever as the largest prime number proven by hand. Later [[Derrick Henry Lehmer]] refined Lucas' primality tests and obtained the [[Lucas-Lehmer test]]. | |||
He worked on the development of the [[umbral calculus]]. | |||
Lucas was also interested in [[recreational mathematics]]. He found an elegant [[Binary numeral system|binary]] solution to the [[Baguenaudier]] puzzle. He more notably invented the [[Tower of Hanoi]] puzzle, which he marketed under the nickname ''N. Claus de Siam'', an [[anagram]] of ''Lucas d'Amiens'', and published for the first time a description of the [[Dots and Boxes]] game in 1889. | |||
Lucas died in unusual circumstances. At the banquet of the annual congress of the ''Association française pour l'avancement des sciences'' a waiter dropped some [[crockery]] and a piece of broken plate cut Lucas on the cheek. He died a few days later of a severe skin inflammation probably caused by [[septicemia]]. Lucas was only 49 years old when he died. | |||
==Works== | |||
* [[:commons:Image:Recherches Sur Plusieurs Ouvrages De Léonard De Pise Et Sur Diverses Questions D’Arithmétique Supérieure, Édouard Lucas (1877).pdf|''Recherches Sur Plusieurs Ouvrages De Léonard De Pise Et Sur Diverses Questions D’Arithmétique Supérieure'']] (1877) | |||
* [http://books.google.com/books?id=_hsPAAAAIAAJ&printsec=toc#PPR3,M1 ''Théorie des nombres''], Tome Premier (1891) | |||
* [http://books.google.com/books?id=Ea8AAAAAMAAJ&printsec=toc#PPP9,M1 ''Récréations mathématiques''] (1894) | |||
* [http://books.google.com/books?id=OBgPAAAAIAAJ&printsec=titlepage ''L'arithmétique amusante''] (1895) | |||
==See also== | |||
* [[Lucas prime]] | |||
* [[Lucas sequence]] | |||
* [[Lucas' theorem]] | |||
* [[Tower of Hanoi]] | |||
==References== | |||
{{reflist}} | |||
* {{MathWorld | urlname=CannonballProblem | title=Cannonball Problem}} | |||
*{{Cite book |last=Williams |first=Hugh C. |year=1998 |title=Édouard Lucas and primality testing |series=Canadian Mathematical Society series of monographs and advanced texts |volume=22 |location=New York |publisher=[[John Wiley & Sons|Wiley]] |isbn=0-471-14852-0 |postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}. | |||
==External links== | |||
* {{MacTutor Biography|id=Lucas}} | |||
* [http://www.cs.wm.edu/~pkstoc/toh.html Scans of Lucas's original Tower of Hanoi puzzle in French, with translations] | |||
* [http://faculty.evansville.edu/ck6/bstud/lucas.html Édouard Lucas], by Clark Kimberling | |||
* [http://edouardlucas.free.fr/ Édouard Lucas] | |||
{{Authority control|VIAF=12311733}} | |||
<!-- Metadata: see [[Wikipedia:Persondata]] --> | |||
{{Persondata | |||
|NAME= Lucas, Édouard | |||
|ALTERNATIVE NAMES= | |||
|SHORT DESCRIPTION=French mathematician | |||
|DATE OF BIRTH=April 4, 1842 | |||
|PLACE OF BIRTH=[[Amiens]], [[France]] | |||
|DATE OF DEATH=October 3, 1891 | |||
|PLACE OF DEATH= [[Paris]] | |||
}} | |||
{{DEFAULTSORT:Lucas, Edouard}} | |||
[[Category:1842 births]] | |||
[[Category:1891 deaths]] | |||
[[Category:19th-century French mathematicians]] | |||
[[Category:Number theorists]] | |||
[[Category:École Normale Supérieure alumni]] | |||
[[Category:Fibonacci numbers]] | |||
[[Category:Recreational mathematics experts]] | |||
[[Category:Deaths from sepsis]] | |||
Latest revision as of 07:10, 12 March 2013
Template:Infobox scientist François Édouard Anatole Lucas (4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him.
Biography
Lucas was educated at the École Normale Supérieure. He worked in the Paris observatory and later became a professor of mathematics in Paris. In the meantime he served in the army.
In 1875, Lucas posed a challenge to prove that the only solution of the Diophantine equation:
with N > 1 is when N = 24 and M = 70. This is known as the cannonball problem, since it can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building a square pyramid out of them. It was not until 1918 that a proof (using hyperelliptic functions) was found for this remarkable fact, which has relevance to the bosonic string theory in 26 dimensions.[1] Elementary proofs have been more recently published.[2][3]
He devised methods for testing the primality of numbers. In 1857, at age 15, Lucas began testing the primality of 2127 − 1 by hand, using Lucas Sequences. In 1876, after 19 years of testing,[4] he finally proved that 2127 − 1 was prime; this would remain the largest known Mersenne prime for three-quarters of a century. This may stand forever as the largest prime number proven by hand. Later Derrick Henry Lehmer refined Lucas' primality tests and obtained the Lucas-Lehmer test.
He worked on the development of the umbral calculus.
Lucas was also interested in recreational mathematics. He found an elegant binary solution to the Baguenaudier puzzle. He more notably invented the Tower of Hanoi puzzle, which he marketed under the nickname N. Claus de Siam, an anagram of Lucas d'Amiens, and published for the first time a description of the Dots and Boxes game in 1889.
Lucas died in unusual circumstances. At the banquet of the annual congress of the Association française pour l'avancement des sciences a waiter dropped some crockery and a piece of broken plate cut Lucas on the cheek. He died a few days later of a severe skin inflammation probably caused by septicemia. Lucas was only 49 years old when he died.
Works
- Recherches Sur Plusieurs Ouvrages De Léonard De Pise Et Sur Diverses Questions D’Arithmétique Supérieure (1877)
- Théorie des nombres, Tome Premier (1891)
- Récréations mathématiques (1894)
- L'arithmétique amusante (1895)
See also
References
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.
I had like 17 domains hosted on single account, and never had any special troubles. If you are not happy with the service you will get your money back with in 45 days, that's guaranteed. But the Search Engine utility inside the Hostgator account furnished an instant score for my launched website. Fantastico is unable to install WordPress in a directory which already have any file i.e to install WordPress using Fantastico the destination directory must be empty and it should not have any previous installation files. When you share great information, others will take note. Once your hosting is purchased, you will need to setup your domain name to point to your hosting. Money Back: All accounts of Hostgator come with a 45 day money back guarantee. If you have any queries relating to where by and how to use Hostgator Discount Coupon, you can make contact with us at our site. If you are starting up a website or don't have too much website traffic coming your way, a shared plan is more than enough. Condition you want to take advantage of the worldwide web you prerequisite a HostGator web page, -1 of the most trusted and unfailing web suppliers on the world wide web today. Since, single server is shared by 700 to 800 websites, you cannot expect much speed.
Hostgator tutorials on how to install Wordpress need not be complicated, especially when you will be dealing with a web hosting service that is friendly for novice webmasters and a blogging platform that is as intuitive as riding a bike. After that you can get Hostgator to host your domain and use the wordpress to do the blogging. Once you start site flipping, trust me you will not be able to stop. I cut my webmaster teeth on Control Panel many years ago, but since had left for other hosting companies with more commercial (cough, cough) interfaces. If you don't like it, you can chalk it up to experience and go on. First, find a good starter template design. When I signed up, I did a search for current "HostGator codes" on the web, which enabled me to receive a one-word entry for a discount. Your posts, comments, and pictures will all be imported into your new WordPress blog.- 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.
External links
- Template:MacTutor Biography
- Scans of Lucas's original Tower of Hanoi puzzle in French, with translations
- Édouard Lucas, by Clark Kimberling
- Édouard Lucas
In the event you've just lately been requested by your employer to be posted to Singapore, then this website is for you. Whether or not you're single or married with kids, whether or not you are looking for a condominium, a bungalow, a semi-detached or a public condo, residing and renting a house in Singapore at this time is straightforward when you recognize the ins and outs, the dos and don'ts.
He is a rip-off!! Severely trust me he's on of the scammer agent. He made me believe that I've a spot to remain then when I was about to move the place isn't out there. Then he just took my deposit and agent's charge. By the best way he's also the landlord of the place i am presupposed to lease. He took my money and ran away. However I went to the HDB and complain him, additionally I complain straight to the police. Then the police called him and he got scared. Finally each penny that I gave him, he give it again since HDB and police office is supporting me. Don't be lazy to complain. Go straight to the police and complain these individuals.
i imagine there are good ethical brokers in Singapore. But i have encounter unhealthy experiencing the Christina Fong from realty master. She is admittedly an unprofessional and never moral one. Only considering of undercutiing and squeezing money from ptther people without defending interest of her personal shopper. Proceed to the section Training and look at a map of all worldwide colleges in Singapore or visit the section residential areas for detailed data on the place to stay and why. Information District and Location Have completed no less than 30 property transactions up to now three years. At least 10 of these transactions will have to be for private properties, and at the very least one other 10 needs to be for HDB flats (also known as public housing); Singapore-Indonesia Commercial Affiliation
Agents need to be very resourceful and so they have to work doubly onerous to succeed in out to extra consumers as a result of when the market swings, it turns into very aggressive," said PropNex Chief Executive Mohamed Ismail. "Beforehand, an agent might focus on one space, comparable to HDB, however at this time you may't." An motion for misrepresentation arises beneath the law of tort. A Misrepresentation happens when the Representor (Property Agent) makes a false assertion of existing truth with data of its falsity and with the intention that the Representee (Buyer or Seller) ought to act on it with the consequence that the Representee does act on it to his detriment. Metropolis & South West (D01-08) Tiong Bahru MRT Quiet C/Room F/Furnished w AC No Agent Price
On February 19 we had an appointment with the proprietor and his agent (A and H!) at the condominium to hand over the keys. They went by means of all the things with a wonderful tooth comb. An important lesson we learned over all this is that you simply MUST ENGAGE YOUR PERSONAL AGENT and never rely on the homeowners agent as his priority is to the proprietor not you. Nevertheless, last night time my own agent called me and informed me suddenly that ECG instructed them a buyer goes handy them a check within the morning, so we higher act fast or we may lose the property. Stamp responsibility is to be paid inside 14 days from the date of acceptance of the OTP or Sale and buy a house in singapore (click hyperlink) (S&P) Settlement. For more information, please go to www.iras.gov.sg - Gown Up Your House Woodlands East Industrial & Industrial Affiliation
There may also be a Code of Ethics and a Skilled Conduct Commonplace, as well as the introduction of disciplinary motion in opposition to errant brokers/businesses and dispute decision mechanisms. Preparations shall be made to manage the transition of existing agencies and agents to these new standards, which have but to be finalized. The Proposed Enchancment in High quality for Actual Property Businesses Wheelock Properties put up 95 items of The Panorama in Ang Mo Kio for balloting. With a reduction of 12 p.c, they claimed to promote 80 to eighty five units. Whereas developers are clearing their existing stock, every month there are new projects acquiring their HIGH and new sites released by the government to construct more private housing. The due date of each rental payment; or
To know who pays actual property commissions - whether or not it's sellers or buyers or both or if it is Landlord's or Tenant's or both Divisions vary. All Brokers work on a commission scheme that is determined by the experience, efficiency and various other elements equivalent to recruitment and many others. New brokers can receive from a range of 60%-70% of the full fee received by them from the closure of a deal. High producing brokers would possibly obtain 100% and pay the company (broker) a desk fee. Everybody else falls somewhere in between. Kindly discuss with the FAQ part of the CEA web site-www.cea.gov.sg Co-Broking / sharing of fee There isn't a set formulation. This is based on the demand and supply circumstances in the market. present agents have tertiary education.
Template:Persondata
- ↑ Template:Cite web
- ↑ 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 - ↑ 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 - ↑ Template:Cite web