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I just wrote a program to investigate 5 fold symmetry in 2d, it generates something akin to penrose tiling. here is a pic and a video on YT: i am not convinced that it can't practically be tiled in a square shape, you may have places where only one triangle is wrong in a frame of 1000 of them or something, else you could find a place with good 4 fold ...


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The command is: $$\mathtt{runif(1,a,b)}$$


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Blender is not a mathematics oriented software but it answers the needs you describe in your example. You can write plugins in Python and run them within Blender to fill up your mathematical needs.


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For a more simplistic graph drawing program, see CMap at http://cmap.ihmc.us. It is a concept modeling tool which has many export and import formats, including a text tab-delimited format for triples (which it calls propositions). CMap is more aligned to non-coders such as k-12 students and college, managers, etc., who want to model (i.e., graphs schemas ...


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This is a fairly technical question, and therefore will admit a technical answer. If $x,y$ are restricted to be real (or rational) numbers, then $\sqrt{-x}$ is undefined for $x>0$. Once we have an undefined quantity, we cannot proceed further, even multiplying it by zero. Hence with this restriction Desmos is correct. However, if $x,y$ are allowed to ...


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Either order is fine. The issue with Desmos is that it is restricting the domain (artificially) to non-positive numbers because $\sqrt{-x}$ is complex for other numbers. In reality, having complex numbers is fine, and indeed, the next step, which is to multiply by zero makes the number real again. Wolfram alpha's plot is more correct, while Desmos' plot is ...



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