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Vedic Mathematics Academy, Main Index. 30 fast mental math Tricks : EasyCal Secrets of Mental Math techniques. Geopersia™ Interactive Girih. Wallpaper group. Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the simpler frieze groups and the three-dimensional crystallographic groups (also called space groups). Introduction[edit] Wallpaper groups categorize patterns by their symmetries. Subtle differences may place similar patterns in different groups, while patterns that are very different in style, color, scale or orientation may belong to the same group. Consider the following examples: Examples A and B have the same wallpaper group; it is called p4m in the IUC notation and *442 in the orbifold notation.
Example C has a different wallpaper group, called p4g or 4*2 . A complete list of all seventeen possible wallpaper groups can be found below. Symmetries of patterns[edit] A symmetry of a pattern is, loosely speaking, a way of transforming the pattern so that the pattern looks exactly the same after the transformation. However, example C is different.
History[edit] Formal definition and discussion[edit] Girih tiling based on a decagonal fractal. My last entry described a girih tiling based on a pentagonal fractal. It's also possible to base a fractal tiling on decagons. This process is simply nesting or subdividing a decagon with five smaller decagons. Starting with a regular decagon, place five smaller regular decagons, edge-to-edge, within the original decagon. One vertex each of the smaller decagons should coincide with a vertex of the larger. Two sides each of the smaller decagons should be edge-to-edge with another small decagon. The lengths of the edges of the smaller decagon are 1/(2x(1+cosine(72))) of the larger. This is the same as calculating the sides of the five smaller decagons by dividing the larger decagon sides by the golden ratio, twice.
Here's a completed girih tiling. ANCIENT MATH of ETHIOPIA - Amazing Methods of Calculation.flv. Trachtenberg system. The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp.
The rest of this article presents some methods devised by Trachtenberg. The most important algorithms are the ones for general multiplication, division and addition[citation needed]. Also, the Trachtenberg system includes some specialized methods for multiplying small numbers between 5 and 13. The chapter on addition demonstrates an effective method of checking calculations that can also be applied to multiplication. General multiplication[edit] The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. Times the next-to-last digit of . Example: Web. What is it like to have an understanding of very advanced mathematics. Techniques for adding the numbers 1 to 100. There’s a popular story that Gauss, mathematician extraordinaire, had a lazy teacher.
The so-called educator wanted to keep the kids busy so he could take a nap; he asked the class to add the numbers 1 to 100. Gauss approached with his answer: 5050. So soon? The teacher suspected a cheat, but no. Let’s share a few explanations of this result and really understand it intuitively. Technique 1: Pair Numbers Pairing numbers is a common approach to this problem. An interesting pattern emerges: the sum of each column is 11. Because 1 is paired with 10 (our n), we can say that each column has (n+1). Which is the formula above. Wait — what about an odd number of items? Ah, I’m glad you brought it up. Let’s add the numbers 1 to 9, but instead of starting from 1, let’s count from 0 instead: By counting from 0, we get an “extra item” (10 in total) so we can have an even number of rows.
Notice that each column has a sum of n (not n+1, like before), since 0 and 9 are grouped. Technique 2: Use Two Rows.