Pierre de Fermat (Born Too Lose)

****** ***** *** Pierre de Fermat *** ***** ***** ***

Born August 17, 1601 Beaumont-de-Lomagne, France Died January 12, 1665 (aged 63) Castres, France Residence France Nationality French Fields Mathematics and Law Known for Number theory Analytic geometry Fermat's principle Probability Fermat's Last Theorem Influences François Viète

* *** **** ******* * Pierre de Fermat * ***** ********* * French pronunciation: [pjɛːʁ dəfɛʁˈma]; 17[1] August 1601 or 1607/8[2] – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality.

In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for Fermat's Last Theorem, which he described in a note at the margin of a copy of Diophantus' Arithmetica. Contents 1 Life and work 1.1 Work 1.2 Death 2 Assessment of his work 3 See also 4 Notes 4.1 Books referenced 5 Further reading 6 External links Life and work Fermat was born in Beaumont-de-Lomagne, Tarn-et-Garonne, France; the late 15th century mansion where Fermat was born is now a museum. He was of Basque origin. Fermat's father was a wealthy leather merchant and second consul of Beaumont-de-Lomagne. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. There is little evidence concerning his school education, but it may have been at the local Franciscan monastery. Bust in the Salle des Illustres in Capitole de Toulouse He attended the University of Toulouse before moving to Bordeaux in the second half of the 1620s. In Bordeaux he began his first serious mathematical researches and in 1629 he gave a copy of his restoration of Apollonius's De Locis Planis to one of the mathematicians there. Certainly in Bordeaux he was in contact with Beaugrand and during this time he produced important work on maxima and minima which he gave to Étienne d'Espagnet who clearly shared mathematical interests with Fermat. There he became much influenced by the work of François Viète. From Bordeaux, Fermat went to Orléans where he studied law at the University. He received a degree in civil law before, in 1631, receiving the title of councillor at the High Court of Judicature in Toulouse, which he held for the rest of his life. Due to the office he now held he became entitled to change his name from Pierre Fermat to Pierre de Fermat. Fluent in Latin, Basque[citation needed], classical Greek, Italian, and Spanish, Fermat was praised for his written verse in several languages, and his advice was eagerly sought regarding the emendation of Greek texts. He communicated most of his work in letters to friends, often with little or no proof of his theorems. This allowed him to preserve his status as an "amateur" while gaining the recognition he desired. This naturally led to priority disputes with contemporaries such as Descartes and Wallis. He developed a close relationship with Blaise Pascal.[3] Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta's new algebraic methods."[4] Work Fermat's pioneering work in analytic geometry was circulated in manuscript form in 1636, predating the publication of Descartes' famous La géométrie. This manuscript was published posthumously in 1679 in "Varia opera mathematica", as Ad Locos Planos et Solidos Isagoge, ("Introduction to Plane and Solid Loci").[5] In Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum, Fermat developed a method for determining maxima, minima, and tangents to various curves that was equivalent to differentiation.[6] In these works, Fermat obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature. Pierre de Fermat Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series.[7] The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.[citation needed] In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers. It was while researching perfect numbers that he discovered the little theorem. He invented a factorization method—Fermat's factorization method—as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. Fermat developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on. Although Fermat claimed to have proved all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical tools available to Fermat. His famous Last Theorem was first discovered by his son in the margin on his father's copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof. He had not bothered to inform even Marin Mersenne of it. It was not proved until 1994, using techniques unavailable to Fermat. Although he carefully studied, and drew inspiration from Diophantus, Fermat began a different tradition. Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equations, and he looked for all possible general solutions. He often proved that certain equations had no solution, which usually baffled his contemporaries. Through his correspondence with Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork for the theory of probability. From this brief but productive collaboration on the problem of points, they are now regarded as joint founders of probability theory.[8] Fermat is credited with carrying out the first ever rigorous probability calculation. In it, he was asked by a professional gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two dice resulted in him losing. Fermat subsequently proved why this was the case mathematically.[9] Fermat's principle of least time (which he used to derive Snell's law in 1657) was the first variational principle[10] enunciated in physics since Hero of Alexandria described a principle of least distance in the first century CE. In this way, Fermat is recognized as a key figure in the historical development of the fundamental principle of least action in physics. The term Fermat functional was named in recognition of this role.[11] Death Plaque at the place of burial of Pierre de Fermat Place of burial of Pierre de Fermat in Place Jean Jaurés, Castres, France. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councilor of the chamber of Edit and mathematician of great renown, celebrated for his theorem (sic), an + bn ≠ cn for n>2 He died at Castres, Tarn.[2] The oldest, and most prestigious, high school in Toulouse is named after him: the Lycée Pierre de Fermat. French sculptor Théophile Barrau made a marble statue named Hommage à Pierre Fermat as tribute to Fermat, now at the Capitole of Toulouse. Assessment of his work Holographic will handwritten by Fermat on 4 March 1660 — kept at the Departmental Archives of Haute-Garonne, in Toulouse Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. According to Peter L. Bernstein, in his book Against the Gods, Fermat "was a mathematician of rare power. He was an independent inventor of analytic geometry, he contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."[12] Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."[13] Of Fermat's number theoretic work, the great 20th-century mathematician André Weil wrote that "... what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with the descent which is rightly regarded as Fermat's own."[14] Regarding Fermat's use of ascent, Weil continued "The novelty consisted in the vastly extended use which Fermat made of it, giving him at least a partial equivalent of what we would obtain by the systematic use of the group theoretical properties of the rational points on a standard cubic."[15] With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers. See also Diagonal form Euler's theorem Fermat cubic Fermat Prize Fermat pseudoprime Fermat quotient Fermat's spiral Fermat's theorem (stationary points) dogmeat

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Quick Tip: Ever Thought About Using @Font-face for Icons?

Wayne Helman on Apr 23rd 2010 with 116 comments

Tutorial Details

• Technology: CSS
• Estimated Completion Time: 15 Minutes
• Difficulty: Beginner

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This entry is part 11 of 16 in the CSS3 Mastery Session - Show All
« PreviousNext »

• 10 CSS3 Properties you Need to be Familiar With
• The 30 CSS Selectors you Must Memorize
• Getting to Work with CSS3 Power Tools
• Mimic Equal Columns with CSS3 Gradients
• A Crash-Course in CSS Media Queries
• The Multi-Column CSS3 Module
• Design a Prettier Web Form with CSS3
• Typography that you'd Swear Was Made in Photoshop
• Detect CSS Support with JavaScript
• CSS3 Transitions: Fundamentals
• Ever Thought About Using Font-Face for Icons?
• The Intricacy of Simplicity
• The State of CSS3 in Email Templates
• Getting Clever with CSS3 Shadows
• Build Awesome Practical CSS3 Buttons
• How to Build a Kick-Butt CSS3 Mega Drop-Down Menu

The evolution of Internet technologies never ceases to amaze. Seemingly daily, new concepts and techniques are being thought up by creative and talented people. With modern browsers being adopted at a greater rate, systems like CSS3 are becoming more and more viable for use on projects of all sizes. Clearly, this can be seen by looking at new services sprouting on-line like TypeKit. Conceptually, if we deconstruct a font down to it’s basic elements, we can make use of this technology for things other than type, icons.

 

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The Need for Speed

For a short period of time, developers began producing websites with little regard for bandwidth consumption. HTML and CSS where restrictive and Adobe Flash was an open canvas for designers and developers to stuff animations and complex layouts into. This resulted in some extremely bandwidth heavy sites—we all remember a few. Those were the days before the proliferation of mobile smart phones.

With smart phones accessing the Internet more frequently, bandwidth and page load speeds have suddenly returned to the forefront. Thankfully, advances in HTML, CSS, and JavaScript have made that all possible. Central to webpage speed and responsiveness is the number of HTTP requests a page load must make. Modern browsers limit the number of requests to a single server. The W3C HTTP 1.1 specification reads

“A single-user client SHOULD NOT maintain more than 2 connections with any server or proxy. A proxy SHOULD use up to 2*N connections to another server or proxy, where N is the number of simultaneously active users. These guidelines are intended to improve HTTP response times and avoid congestion.”

One technique that has become increasingly popular is the use of CSS sprites. CSS sprites are designed to reduce the number of HTTP requests to the web server by combining many smaller images into a single larger image and defining a block level CSS element to only show a defined portion of the larger image. The technique is simple, but ingenious.

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Deconstructing the Font

Fonts at their most basic molecular level are a series of vector glyphs packaged up into a single “glyph archive”.

CSS3 has introduced to the web development world the ability to embed fonts with the @face-face declaration. Without question, this advancement in Internet technologies is one of the most exciting and important stages in our brief history. With developers able to embed fonts of their choice, designers can produce layouts that will render far more consistently from platform to platform bringing the art of interactive layout closer to it’s print cousin.

If we take a closer look at the technology behind a font, we can gain a far better understanding of how they can be used and deployed. Fonts at their most basic molecular level are a series of vector glyphs packaged up into a single “glyph archive”. We can then reference each glyph by its corresponding character code. Theoretically, it’s very similar to the way in which we reference an array in almost any programming language—through a key/value pair.

With this in mind, the glyphs we reference can really be any vector-based single color image. This is nothing new—we’ve all seen Dingbats and Webdings. They are two examples of non-type fonts, that is, a series of vector based images compiled into a single font archive.

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Abstracting and Expanding @font-face

With the advent of font embedding and the realization that fonts are essentially a series of simple vector glyphs, I began to experiment on how to use this format to my advantage. Conceptually, if I placed all required icons for a particular site into a custom font, I would then be able to use those icons anywhere on the site with the ability to change size and color, add backgrounds, shadows and rotation, and just about anything else CSS will allow for text. The added advantage being a single CSS sprite-like HTTP request.

To illustrate, I’ve compiled a new font with a few of the great icons from Brightmix.

I’ve used the lower case slots for plain icons, and the uppercase slots for the same icon in a circular treatment.

To use my new Icon Pack, I’ll first have to export my font set as a number of different font files (.eot, .woff, .ttf, .svg) to be compatible with all browsers. The topic of font embedding and file format converting is covered elsewhere, so I will avoid a detailed explanation here. However, the CSS would look something like this.

view plaincopy to clipboardprint?

1. @font-face {  
2.   font-family: 'IconPack';  
3.   src: url('iconpack.eot');  
4.   src: local('IconPack'),  
5.     url('iconpack.woff') format('woff'),  
6.     url('iconpack.ttf') format('truetype'),  
7.     url('iconpack.svg#IconPack') format('svg');  
8. }  

@font-face { font-family: 'IconPack'; src: url('iconpack.eot'); src: local('IconPack'), url('iconpack.woff') format('woff'), url('iconpack.ttf') format('truetype'), url('iconpack.svg#IconPack') format('svg'); }

Once embedded, I now have a complete icon set in vector format to reference. To reference an icon I simply need a style that includes the font-family of “IconPack”.

image alt tag

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Posted: 16 Aug 2011 06:38 AM PDT

 

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Hi Gaejang, Here is this week's summary for your Facebook Pages:   I quit eating Sparta 1,551 monthly active users103 since last week 1,122 people like this2 since last week 18 wall posts or comments this week8 since last week 320 visits this week1,868 since last week Send an update to people who like this Visit your Insights Page Promote with Facebook Ads Dampira Quin (Band) 45 monthly active users2 since last week 112 people like this0 since last week 0 wall posts or comments this week0 since last week 29 visits this week13 since last week Send an update to people who like this Visit your Insights Page Promote with Facebook Ads 주아란 (Parry Hotter) 72 monthly active users1 since last week 75 people like this0 since last week 0 wall posts or comments this week3 since last week 21 visits this week4 since last week Send an update to people who like this See the full gallery on Posterous Visit your Insights Page Promote with Facebook Ads Dogmeat Page 4,353 monthly active users138 since last week 67 people like this0 since last week 3 wall posts or comments this week3 since last week 58 visits this week9 since last week Send an update to people who like this Visit your Insights Page Promote with Facebook Ads Learn more about how to update via mobile   Statistics and management for additional Pages   Thanks, The Facebook Team

 

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@Font-Face Icon et Le Template French Fou!   Posted: 16 Aug 2011 11:40 AM PDT   Layout Zoom: Increase | Decrease Dogmeat's gone @font-face icon French Template Crazy! @Font-Face Icon et Le  Template French Fou! technology philosophy tags territory tools schedule Lorem ipsum dolor sit amet   Tutorial ...»See Ya

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FOUND! Best html5 SVG Site-links in one place! Thanks Frenchy!

Note for English speaker, there is an English version down below

Le 27 mai dernier, j’ai eu la chance de participer à la toute première édition de SudWeb à Nîmes. Partie sur une boutade lors du dernier Paris Web, les organisateurs se sont juste arrachés pour arriver à monter le truc en à peine 6 mois. Bravo à tous, ce fût beau ! Car on peut le dire, pour un coup d’essai, ce fût un coup de maitre. Au delà de la logistique impeccable, l’ensemble du programme des conférences était tout simplement parfait. Mixant à la fois les aspects fonctionnels, techniques et prospectifs, l’équilibre du déroulé m’a complètement estomaqué (ainsi que le respect des horaires, tenus d’une main de fer, couplé à des moments de pause ô combien conviviaux).

Vous n’y étiez pas ? Ce n’est pas grave. D’une part toutes les conférences ont été filmées et devraient être disponibles prochainement et d’autre part, il y aura une autre édition l’année prochaine, viendez-y

En ce qui concerne mon nombril, j’ai eu l’occasion d’y donner une conférence sur un sujet qui me tient à cœur depuis un peu plus d’un an : SVG. Au cours de cette conférence, j’ai montré ce qu’il était possible de faire aujourd’hui avec SVG (qui, rappelons le, est disponible dans tous les navigateurs moderne). Plutôt que de m’attacher aux questions techniques qui tourne autour de cette technologie, j’ai préféré mettre l’accent sur des outils et des résultats concrets. L’idée étant de montrer comment des designers et les développeurs on déjà utilisé SVG et ce qu’il apporte au web design moderne.

Évidemment, même si j’ai oublié de le préciser pendant la conférence, je n’ai pas pu m’empêcher de réaliser mes slides en SVG, les voici (cliquez sur l’image pour lui donner le focus et utilisez les flèches de direction pour passer d’un slide à l’autre) :

A noter que je cite tous les sites suivant :

Outils

• http://code.google.com/p/svgweb
• http://raphaeljs.com : Vous devriez tous avoir cette bibliothèque dans votre trousse à outils si vous voulez réaliser du SVG tout en étant compatible avec les vieux IE.
• http://www.highcharts.com : LA bibliothèque pour faire des graphiques de données sans vous casser la tête.
• http://mbostock.github.com/d3/ : D3.js est une bibliothèque qui vous permet de mapper des données au seins de graphiques vectoriels en SVG. C’est un pont technique idéal entre les développeurs qui doivent manipuler ces données et les designers qui doivent les mettre en scène.

Références

• http://www.thenounproject.com : Projet mettant à disposition des icones libres de droit au format SVG. Indispensable pour réaliser de la signalétique. A noter que toutes les icones proposées sont composées d’un seul est unique chemin SVG ce qui en fait une base travail extrêmement propre et malléable pour les Web designers.
• http://www.bifter.co.uk : Web comics humoristique intégralement réalisé en SVG.
• http://opendata.zeit.de/pisa-wohlstands-vergleich/visualisierung.php : Le journal allemand Zeit propose une visualisation de données démographiques intégralement réalisée en SVG
• http://www.nissanusa.com/leaf-electric-car/index : Dans la série “Non, ce n’est pas du Flash” Nissan USA fait une magnifique utilisation de SVG pour proposer une navigation non linéaire des caractéristiques de sa nouvelle voiture électrique. A noter que RaphaelJS est utilisé pour assurer la compatibilité avec IE6, 7 et 8 (et oui).
• http://rickardsund.com : Je n’ai pas de mot assez fort pour exprimer l’adoration que j’ai pour ce site. Pour moi, Il représente la quintessence du Web design moderne. D’un coté un design épuré à l’extrême qui sert parfaitement son propos. Il est l’œuvre de Hugo Ahlberg qui a un lourd passif de designer Flash, ce qui lui a permis de s’extraire des contraintes (artificielles) du design web traditionnel. D’un autre coté, il est intégré à la perfection en utilisant exclusivement des standards Web : HTML5 (à noter en particulier la magnifique utilisation de l’API History), CSS3, JS (Du “mouse gesture” de toute beauté) et bien sur du SVG (par petites touches mais indispensables). Ce travail formidable a été réalisé par Daniel Mahal et Daniel Connor qui font là une démonstration d’excellence de ce que devrais toujours être une intégration aux standards, en particulier la maitrise de la dégradation élégante qui est quasi parfaite : Ce site fonctionne dans IE6 ! Vous DEVEZ regarder la source de ce site et vous en inspirer.

Pour conclure, je n’ai plus qu’une chose à dire : Longue vie à SudWeb, vivement l’année prochaine

On May 27th, I got the chance to attend the very first SudWeb event in Nîmes, France. Starting on a joke during the last Paris Web event, the people behind SudWeb make it possible in just 6 months. Thanks dudes that was awesome! We can say it, for a first run that was a master piece. Beyond the perfect logistic, the program was just great. Talks were amazingly well balanced between functional, technical and prospective subjects (and the schedule was perfectly mastered with good time to talk and network with people).

You wasn’t their ? Don’t worry. First, all the talks were camcorded and should be available soon. Second, there will be another edition next year, attend it

On my own, I had the opportunity to give a talk about one of my favorite subject for a year now : SVG. During this talk, I show off what is it possible to make with SVG today (which, as a reminder, is available in all modern browsers). Instead of talking about technical stuffs, I focused on tools and practical results. The idea was to demonstrate how designers and developers had used SVG and what that technology brings to modern Web design.

Of course, even if I forgot to mention it during my talk, I felt oblige to made my slides with SVG. Here there are (see above, click on the image to give it the focus then use the arrow keys to switch between the slides).

Note that I use all the following web sites as examples:

Tools

• http://code.google.com/p/svgweb
• http://raphaeljs.com : You should all have that library in your toolbox if you want to use SVG with IE compatibility in mind.
• http://www.highcharts.com : THE library to build charts without headache.
• http://mbostock.github.com/d3/ : D3.js is a library that allow you to connect data with graphics. This is an awesome bridge between developers that deal with data and designer that deal with graphics.

References

• http://www.thenounproject.com : That project collect visual symbol and make them available in SVG. Note that all the symbols are made of one single SVG path. That make them highly usable as a work basis for Web designers.
• http://www.bifter.co.uk : A humorous Web comics build with SVG.
• http://opendata.zeit.de/pisa-wohlstands-vergleich/visualisierung.php : The dutch newspaper Zeit had a demographic data representation driven by SVG.
• http://www.nissanusa.com/leaf-electric-car/index : Ok, so “This is NOT Flash”. This is a great SVG work made by Nissan USA to build a non-linear navigation system. Take care about the library behind the scene, it’s RaphaelJS. This means that it works properly even with IE6, 7 and 8 (crazy!).
• http://rickardsund.com : I do not have strong enough words to express my love for this web site. To me, it’s the best of modern Web design. On the one hand, the simplistic design suits its subject perfectly. It has been made by Hugo Ahlberg who has extensive skills in Flash design. Those skills give him the ability to overcome the classic HTML web design. On the other hand, This Web site is perfectly develop with Web standards only : HTML5 (with a noticeable use of the History API), CSS3, JS (awesome mouse gesture) and, of course, some small (but essential) touches of SVG. This amazing work has been done by Daniel Mahal and Daniel Connor who demonstrate what a Web standards front-end development should always be. They especially mastered the graceful degradation: This site works perfectly with IE6 ! You SHOULD look at the source and use it as an inspiration.

To conclude, there is one thing left : Live long SudWeb, I strongly hope for the next edition

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Note for English speaker, there is an English version down below Le 27 mai dernier, j’ai eu la chance de participer à la toute première édition de SudWeb à Nîmes. Partie sur une boutade lors du dernier Paris Web, les organisateurs se sont juste arrachés pour arriver à monter le truc en à peine 6 moi ...»See Ya