background preloader

A Visual, Intuitive Guide to Imaginary Numbers

A Visual, Intuitive Guide to Imaginary Numbers
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories: It’s a mathematical abstraction, and the equations work out. Deal with it.It’s used in advanced physics, trust us. Just wait until college. Gee, what a great way to encourage math in kids! Focusing on relationships, not mechanical formulas.Seeing complex numbers as an upgrade to our number system, just like zero, decimals and negatives were.Using visual diagrams, not just text, to understand the idea. And our secret weapon: learning by analogy. It doesn’t make sense yet, but hang in there. Video Walkthrough: Really Understanding Negative Numbers Negative numbers aren’t easy. But what about 3-4? Negatives were considered absurd, something that “darkened the very whole doctrines of the equations” (Francis Maseres, 1759). What happened? Rather than saying “I owe you 30” and reading words to see if I’m up or down, I can write “-30” and know it means I’m in the hole. Uh oh. Wrong. or Related:  MathématiquesOutlawEducation 2

Norme (mathématiques) Un article de Wikipédia, l'encyclopédie libre. Si et sont deux points du plan ou de l'espace usuel, la norme du vecteur est la distance c'est-à-dire la longueur du segment . La norme, la direction et le sens sont les trois données qui caractérisent un vecteur et qui ne dépendent donc pas du choix du représentant. La norme usuelle d'un vecteur peut se calculer à l'aide de ses coordonnées dans un repère orthonormé à l'aide du théorème de Pythagore. La norme ne s'annule que pour le vecteur nul .La norme du produit par un nombre est le produit de la norme par la valeur absolue de ce nombre : En particulier, tout vecteur a la même norme que son opposé : Soient K un corps commutatif muni d'une valeur absolue et E un K-espace vectoriel. Une norme sur E est une application sur E à valeurs réelles positives et satisfaisant les hypothèses suivantes : Remarques. Les corps des réels et des complexes ne sont pas les seuls à admettre une valeur absolue. Cette topologie possède la propriété suivante : un vecteur

Ideas as Living Organisms - The Daniel Dennett Keynote Discusses How Thoughts are Alive In an evocative and humorous Daniel Dennett keynote, the author and philosopher discusses human evolution and the impact that the spreading of concepts and the discovery of new doctrines can have on those who are exposed to them. He discusses the power of ideas and the way that communication functions as a meme because it is impacted by cultural and societal interactions. The resounding idea he proposes is that human communication and thoughts should be seen as organisms that are literally alive in their own right. According to the academic, thought transmission is a powerful and sometimes dangerous thing that should be treated as a living and breathing being. Stats for Ideas as Living Organisms Trending: Older & Chilly Traction: 549 clicks in 189 w Interest: > 3 minutes Concept: Daniel Dennett Keynote Related: 13 examples / 10 photos Segment: Neutral, 18-55+ Comparison Set: 5 similar articles, including: the inception of good ideas, breakthrough thinking, and new science of memory.

MIT's free online classes can carry credit The Massachusetts Institute of Technology has offered free online courses for the last four years with one major downside: They didn't count toward a degree. That's about to change. In a pilot project announced Wednesday, students will be able to take a semester of free online courses in one of MIT's graduate programs and then, if they pay a "modest fee," earn a "MicroMaster's" degree, the school said. The new degree represents half of the university's one-year master's degree program in supply chain management. The fee for the MicroMaster's degree amounts to what it now costs to receive a "verified certificate" for finishing online classes, the university said. "The rising cost of education, combined with the transformative potential of online teaching and learning technologies, presents a long-term challenge that no university can afford to ignore," MIT President L. MIT didn't immediately say when the new pilot project would launch.

Algèbre géométrique Un article de Wikipédia, l'encyclopédie libre. Paul Tannery popularise l'expression « algèbre géométrique ». En mathématiques, l’algèbre géométrique regroupe des méthodes géométriques, utilisées par les Grecs de l'Antiquité, pour établir des résultats maintenant classés dans la branche mathématique appelée algèbre. Si ces méthodes sont anciennes et correspondent à une vision des mathématiques qui n'est plus la nôtre, elles sont toujours utilisées dans l’enseignement, soit pour donner des preuves simples de certains résultats, soit pour développer une conscience intuitive de résultats qu'une présentation algébrique rendrait plus abstraits. Le terme « algèbre géométrique » provient d’un livre de l’historien des sciences Hieronymus Georg Zeuthen (en) écrit en 1902. Propriétés de la multiplication[modifier | modifier le code] Nombre entier positif[modifier | modifier le code] La multiplication est distributive par rapport à l'addition. Fraction[modifier | modifier le code] ↑ Charles-E.

Talismans - Jackie Chan Adventures Wiki - Wikia The Talismans of Shendu are named for the twelve animals of the Chinese zodiac. They each hold an aspect of Shendu's power. History Long ago, Shendu's subjects rose up against him, led by Lo Pei, Using an extraction spell, he trapped Shendu in statue form, separating his powers from him in the form of twelve Talismans. Lo Pei scattered them across the globe to make sure Shendu that would never again rise to power. It would be nine centuries before Shendu made a deal with the Dark Hand in exchange for treasure. Near Hong Kong, at Shendu's palace, Jackie used a potion dabbed on his hands to extract the Rat Talisman and turn Shendu back into a statue, which Jade destroyed with the Dragon Talisman. Later, the J-Team was able to recover the Talismans and had them locked in Section 13, from which they would make cameo appearances in all of the later seasons as characters (usually Jade) used them for various tasks. Twelve Talismans The Talisman Powers Trivia

Hillary Clinton to unveil $350-billion plan to make college more affordable Hillary Rodham Clinton outlined a plan Monday to slash student loan interest rates while aiming to guarantee students could attend college without needing to take out loans in the first place, tapping into an issue that has risen in prominence among Democrats. Under Clinton’s plan, state governments, higher education institutions and students would play roles alongside the federal government in addressing the affordability of higher education and the debt that can come from it. “We need to make a quality education affordable and available to everyone willing to work for it without saddling them with decades of debt,” she said. The $350-billion plan Clinton outlined at a New Hampshire town hall meeting was the most expensive and expansive policy proposal of her campaign thus far. States that agree to increase spending on higher education would be eligible for federal grants to help reduce the gap between what families can afford to pay and full tuition. Sen. Former Maryland Gov.

Alhazen Un article de Wikipédia, l'encyclopédie libre. Alhazen Alhacen, Alhazen ou Ibn al-Haytham, de son vrai nom Abu Ali al-Hasan ibn al-Hasan ibn al-Haytham[1] (Bassora, 965 – Le Caire, 1039) est un mathématicien, philosophe et physicien du monde médiéval arabo-musulman[2]. Un des premiers promoteurs de la méthode scientifique expérimentale, mais aussi un des premiers physiciens théoriciens à utiliser les mathématiques, il s'illustre par ses travaux fondateurs dans les domaines de l’optique physiologique et de l'optique. Certains, pour ces raisons, l’ont décrit comme le premier véritable scientifique, héritier des scientifiques grecs et indiens. Biographie[modifier | modifier le code] Alhazen est né en 965 à Bassora dans l’actuel Irak où il reçut une éducation qu’il compléta cependant dans la ville de Bagdad. Alhazen commença sa carrière de scientifique dans sa ville natale de Bassorah. Après la mort du calife Hakim, en 1021, Alhazen cessa de feindre sa folie et put sortir de sa résidence.

Become Obsessed to the Point of Madness Do you want to know the secret to giving up all of your vices? Do you know why you have a bunch of bad habits in the first place? I will tell you why, and my answer isn’t the one self-help gurus will give. There is a sad secret that you won’t admit to yourself. You have vices because you are aimless. You are simply existing. I have a solution. It is a solution that every loser and hater will tell you is wrong. Become obsessed. Obsession is Not a Bad Word. Losers will tell you that obsession is a bad thing. (“Will wife/daddy/the boss man let me play with my train set later?”) Here is what occupies the thoughts of the average man: What is my girlfriend/wife doing right now? The average man is just trying to fill up his day with distractions. (There is no danger. Become Obsessed with Excellence. Let me tell you what happened when I became obsessed with taking Danger & Play to the next level. Because I am on a mission, it doesn’t taken me any willpower at all to rid myself of these filthy habits.

Privately educated graduates 'earn more' than state school colleagues - BBC News Privately educated UK graduates in high status jobs earn more than their state school counterparts, says a study. The report, by the Sutton Trust and UpReach, examined those in careers such as law and financial services. It found that, on average, three years after graduation, those who attended fee-paying schools earned £4,500 more. The government said it was "determined... to ensure every child, regardless of background, reaches their potential" through its policies. The report put the earnings gap down to factors such as the university attended, but also suggested non-academic factors, such as assertiveness, were at play. The research also found salaries of the privately-educated increased more quickly, growing by £3,000 more over the same three-and-a-half year period. Average salaries, six months after graduation, were more generous for those who had attended independent schools - £24,066 compared to £22,735, a difference of £1,331.

Le devenir du nombre (pour lecteur curieux) • Stock • Notre sélection, Il est des essais qui savent nommer la nervure conceptuelle de l’époque. Le Devenir du nombre est de ceux-là : une méditation métaphysique composée par l’écrivain Mathieu Terence qui décrit un temps, le nôtre, déserté par l’incalculable. Le Nombre – et avec lui « sa puissance d’abstraction, de quantification et d’uniformisation » – s’est substitué au Verbe. La société est devenue le Fonctionnement. Et la modernité s’efface devant la Technosmose. Terence cerne ainsi la logique de la dépossession de notre liberté d’être par le calcul.

Why the Law of Attraction doesn’t work The Law of Attraction, promulgated in The Secret, became immensely popular when The Secret was first published several years ago. Feeding on people’s greed, The Secret basically said that you can attract whatever you want in your life – money, success, the perfect relationship, great house, car etc – simply by focusing on it with the positive intent to have it. In other words, by using positive intention, or positive thinking, you can manifest whatever you want for your life. Positive thinking has actually been around for decades – it was the basis of the very successful self-help empires of Napoleon Hill, Vincent Peale and Dale Carnegie – the forerunners of new age thinking applied to success in your personal life. Every ‘new’ formula for success based on positive thinking is always a hit – after all, who wouldn’t want an easy way to get rich? In the rush to get on the band wagon, however, very few stop to wonder, if it were so easy, how come everyone is not living out their dream? No.

Teacher grade forecasts are 'too optimistic' - BBC News Teachers are often too optimistic when predicting pupils' grades, suggests a new analysis of exam board data. In future, these forecasts will be crucial to universities when offering places to pupils. That is because A-levels results in in England will depend solely on exams taken at the end of two years' study. The forecasts "will be the only thing universities will have to go on", said Cherry Ridgway of the Association of Teachers and Lecturers (ASCL). But the accuracy of teachers' forecasts is falling, the study suggests. The researchers compared GCSE and A-level results from the OCR board with predictions sent in by teachers just before the exams. At A-level some 43% were correct in 2014, down from 48% in 2012 For GCSEs, 44% of predictions were accurate in 2014, compared with nearly 47% in 2013. New exams Currently universities use AS-level results when making offers - but from next year they will no longer count towards the final A-level grade. Selective schools

Related: