8 math talks to blow your mind Mathematics gets down to work in these talks, breathing life and logic into everyday problems. Prepare for math puzzlers both solved and unsolvable, and even some still waiting for solutions. Ron Eglash: The fractals at the heart of African designs When Ron Eglash first saw an aerial photo of an African village, he couldn’t rest until he knew — were the fractals in the layout of the village a coincidence, or were the forces of mathematics and culture colliding in unexpected ways? Here, he tells of his travels around the continent in search of an answer. How big is infinity? There are more whole numbers than there are even numbers … right? Arthur Benjamin does “Mathemagic” A whole team of calculators is no match for Arthur Benjamin, as he does astounding mental math in the blink of an eye. Scott Rickard: The beautiful math behind the ugliest music What makes a piece of music beautiful?
Visualizing Basic Algebra Last weekend, I shared some interesting properties of numbers with my kids. The great thing about explaining something to a non-expert is that you have to actually understand the topic. (This is why making teaching universities and research universities the same actually makes sense.) If you hide behind a formalism, the explanation won’t work. Usually, this means that you didn’t understand why the formalism worked either. This is why I thought “why are far away things smaller?” Some of the interesting properties of numbers are: that (n + 1)×(n-1)=n2-1: that the perfect squares (0,1,4,9,…) go up by successive odd numbers (1,3,5,…); and that the area of a triangular number (1+2+…+n) has a closed form. Multiplication and division are grounded in visuospatial concepts, which is why these number theoretical results are easy to understand. Properties of Addition Addition is associative: and commutative: Multiplication is Commutative The commutative law is that a×b=b×a. Distributive Law ! Addendum
The Progressive Realist | a metablog about American foreign policy Ed note. This is a guest post by Toby Lanzer, the Deputy Special Representative of the Secretary General for South Sudan (Juba, South Sudan) — As the conflict in South Sudan reached its 100th day, images of death, destruction and displacement in the world’s newest nation continued to dominate the image of the country. The fighting between government and opposition forces has driven a million people from their homes, including about 70,000 who are sheltering in UN peacekeeping bases. We know the situation will worsen with the onset of the rainy season; seven million people are facing the risk of hunger. On April 12, in Washington, DC, USAID, UN humanitarian partners and the European Union will once again focus attention on the crisis, calling for an end to the fighting and urging the international community to continue to fund urgent needs there.
inspq.jpg (JPEG Image, 500x362 pixels) for A level students A Gentle Introduction To Learning Calculus I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity). It all fits together. Calculus is similarly enlightening. They are. Unfortunately, calculus can epitomize what’s wrong with math education. It really shouldn’t be this way. Math, art, and ideas I’ve learned something from school: Math isn’t the hard part of math; motivation is. Teachers focused more on publishing/perishing than teachingSelf-fulfilling prophecies that math is difficult, boring, unpopular or “not your subject”Textbooks and curriculums more concerned with profits and test results than insight Poetry is similar.
WordPress Slider & Gallery Plugin | SlideDeck 1st Medical Studies on Pot in 20 Years Find It Does Relieve Pain Even as California sinks under a massive budget crisis, the $8.7 million the state used to research the use of marijuana for medical purposes now seems money well spent. The state-funded Center for Medical Cannabis Research at the University of California, San Diego has confirmed that pot is effective in reducing muscle spasms associated with multiple sclerosis and pain caused by certain neurological injuries or illnesses, according to a report issued Wednesday [The New York Times]. In four clinical trials, participants suffering from multiple sclerosis, AIDS or diabetes, along with healthy volunteers injected with a chili pepper substance to induce pain, were randomly assigned to receive cigarettes filled with marijuana [The New York Times]. The federal government currently views marijuana as an illegal substance with no medical value–but this unusual set of studies sanctioned by California could cause lawmakers to question that categorization. Image: Flickr/ Neeta Lind
Free A Level Maths Revision and Study Notes from MrBartonMaths Welcome to > pupils > notes for a level I have put together the following selection of excellent resources to help you prepare for your A Level exams. The notes are particaulry useful if you save them to your phone or tablet, so you have your notes with you wherever you are. Happy revising! Please Note: Some of these resources are for specific exam boards. AQA Past Papers and full written solutions - click here Please Note: although these are for AQA, much of the content is the same as other exam boards, so you may still find them useful for extra practise Revision and Exam Tips - click here I have put together a collection of tips and advice for preparing for and sitting your exams Core 1 For more Widgits like this, click here Core 2 Core 4 <A HREF=" Statistics 1 Statistics 2 Statistics 3 Stats 3 Revision Notes from Simon Baxter at Shrewsbury International School, Bangkok Mechanics 1 Mechanics 2 Mechanics 3 Decision 1 Further Pure 1 Further Pure 2 Further Pure 3
Pascal's Triangle Patterns Within the Triangle Using Pascal's Triangle Heads and Tails Pascal's Triangle can show you how many ways heads and tails can combine. For example, if you toss a coin three times, there is only one combination that will give you three heads (HHH), but there are three that will give two heads and one tail (HHT, HTH, THH), also three that give one head and two tails (HTT, THT, TTH) and one for all Tails (TTT). Example: What is the probability of getting exactly two heads with 4 coin tosses? There are 1+4+6+4+1 = 16 (or 24=16) possible results, and 6 of them give exactly two heads. Combinations The triangle also shows you how many Combinations of objects are possible. Example: You have 16 pool balls. Answer: go down to the start of row 16 (the top row is 0), and then along 3 places (the first place is 0) and the value there is your answer, 560. Here is an extract at row 16: A Formula for Any Entry in The Triangle Notation: "n choose k" can also be written C(n,k), nCk or even nCk.
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