Tag: mathematical visualization
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Another Graph Paper Tiling
Advertisements Below is the beginning of a second Quasi-Penrose tiling I’ve made using virtual graph paper and an irregular pentagon created and flipped thereon.
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The Odd Integers 3 Through 129
Advertisements Arranged as Red Squares on a Square Grid Artistically Arranged According to Their Differences-of-Squares Expression Based on Their Ceiling Squares
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More Visualization
Advertisements Here are icons for the odd integers from 3 to 65, based on the differences of each with their ceiling squares (the smallest perfect square greater than their value). The integer corresponding to an icon is the number of red 1×1 squares in that icon.
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Today’s Mathematical Visualization
Advertisements This is an artistically arranged grid-based drawing of the first 24 odd integers greater than 1, expressed as differences of squares – to include the first odd positive integer to have two different “non-trivial” factorizations, and thus two different square-difference representations.
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Adjusted Scatter Plot for Integer Factorization Study
Advertisements The plot below is similar to the one I put in my previous post. However, the data points are, I think, a better set for exposing properties, since I am using the concept of Adjusted Ceiling Square as follows: Let m be an odd positive integer. Define the Adjusted Ceiling Square of m as…
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Integer Factorization: A More Uniform Test, and a Similar Result
Advertisements For 100 pairs of randomly-chosen p and q less than 100,000,000: the Perl routine factor_it_4.pl performed as shown in the following scatter plot of m=pq vs. the number of iterations it required to factor m: Notice, as I mentioned in my blog post about the previous, less uniform test, that the number of iterations…
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Integer Factorization: Performance Stats/Graphs for factor_it_4.pl
Advertisements I ran factor_it_4.pl tonight on the collection of 10-digit and 12-digit discrete semiprimes I had generated earlier in my study. An image of the table I generated is below, along with scatter plots of particular behaviors. If someone wanted, I could certainly supply them with the raw data used to generate the graphs. I…
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Integer Factorization: Recent Work
Advertisements Ideas kept me up when the dogs got me up around 3 a.m. this morning for a walk and some water. That’s good, even though the ideas did not pan out to much. I had church to attend in a few hours, after all. But it occurs to me to share where it’s all…