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{{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 06:10, 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
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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
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Template:Persondata
- ↑ Template:Cite web
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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