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3D Imaging: A Practical Use of Mathematics
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 3D imaging used in dentistry. Once a panoramic x-ray is taken, the technician uses software to rotate the image; the software uses matrix mathematics to compute the position of the rotated image.One use for matrix math is in programming 3D engines for video games. A single point on the screen can be defined as a vector. The TV or computer screen is two-dimensional only, so to create the look of depth, objects must change size as they come closer to the viewer or go farther back into the scene. An image is made up of hundreds or thousands of vectors. By multiplying this set or matrix, you can change its size. You can also multiply the vector array by another array, which allows you to rotate the image. In rotation, parts of the image become ...
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2033 |
bio_man |
10 months ago |
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Simulating the evolution of aggression
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This video brings to life the evolution of aggresive behavior in a population, and its relation to game theory – the field of mathematics concerned with quantifying strategic behavior and decision-making. The author illustrates what happens in an artificial population of species that exhibit two entirely different strategies as they compete for resources. In the first strategy called ‘dove’, organisms are required to share their food source with the other if both happen to land at the same site after being randomly shuffled. Sharing your food source allows the organism to survive another cycle, but not reproduce, unless they’re fortunate enough to land at a site all by them self. The author shows that if this cooperative strategy is ...
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3673 |
duddy |
2 years ago |
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Top 5 Interesting Math Facts You Never Knew
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1) Roman Numeral IVAlthough the Roman numeral for the number 4 has always been taught to have been "IV," according to historians, the ancient Romans probably used "IIII" most of the time. This is partially backed up by the fact that early grandfather clocks displayed IIII for the number 4 instead of IV. Early clockmakers apparently thought that the IIII balanced out the VIII (used for the number 8) on the clock face and that it just looked better. 2) Base 60The Babylonians wrote numbers in a system that used 60 as the base value rather than the number 10. They did not have a symbol for "zero." 3) Fraction BarThe Romans did not use numerals to indicate fractions but instead used words to indicate parts of a whole. It wasn't until later in h ...
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1229 |
bio_man |
5 years ago |
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The 10 Steps to Better Test-Taking
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Once you begin a test, follow these 10 steps to better test-taking.You need to have a game plan to take a math test. This plan is different from plans for taking history, English, humanities, and some science tests. Once you begin a test, follow these 10 steps to better test-taking. The game plan is to get the most points in the least amount of time. Many students lose test points because they use the wrong test-taking strategies for math. By following these ten steps, you can demonstrate more knowledge on the test and get more questions right. Step 1Use a memory data dump. Upon receiving your test, turn it over and write down the information that you put on your mental cheat sheet. Your mental cheat sheet has now turned into a mental list a ...
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4822 |
bio_man |
6 years ago |
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Marathon Problems
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You've all experienced the 30-minute test problem. How to tackle it?With all due respect to essay questions, math, science and engineering students can't tip-toe their way around answers. Test questions are most often multiple choice or free response… and don't let the "free" fool you – there is only one correct answer. Besides "That test sucked," the most common complaint I've heard exiting the myriad math-based tests I've taken over the years is, "You know that long problem at the end? I didn't even know where to start. SO unfair." I think what's really unfair is that person's right to use the same language as the rest of us… but I digress. Truth be told, it's safe to say we've all had our trying times with lengthy, intricate word problems w ...
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996 |
bio_man |
7 years ago |
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How the Turing machine works
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A Turing machine is a hypothetical machine thought of by the mathematician Alan Turing in 1936. Despite its simplicity, the machine can simulate ANY computer algorithm, no matter how complicated it is. Put simply, the Turing machine isn't a physical machine, but you can imagine it as an never-ending line of tape, broken down into squares. On each of those squares is a 1, a 0, or nothing at all. The machine reads one square at a time, and depending on what it reads, it performs an action - it either erases the number and writes a new one before moving on, or simply moves on to a different square. Each of those actions, which mathematicians call a 'state', are determined by the mathematical algorithm or problem the Turing machine has been desi ...
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4830 |
duddy |
7 years ago |
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All trees, regardless of size, break once this wind speed is reached
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The magic number is 42 m/s (94 mph). Using mathematical data and physical experiments, scientists say they have found the law that governs the resistance of wooden beams under stress. According to the study ( link), researchers hung weights from wooden rods and pieces of pencil lead to record the amount of force needed to snap the cylinder. As one might sense, they found that for a fixed length, increasing the diameter made the rods stronger: They could bend more before breaking. This would make tall skinny trees most vulnerable, but, as the team points out, trees don’t grow taller without getting disproportionately thicker as well. By incorporating established laws of tree allometry - which explain the relationship of tree size parameters ...
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12775 |
duddy |
8 years ago |
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