I may be late to the discussion but as regards the Venn Diagrams there is an early stage software you might find useful:
https://penrose.cs.cmu.edu/ https://github.com/penrose It might be incorporated in to Sage (maybe?). Just wanted to add a quick note. Best regards, Furkan Semih. On Sat, Jun 11, 2022 at 6:20 AM Tanmay Kulkarni <[email protected]> wrote: > Hello all, > > My name is Tanmay Kulkarni and I am a rising sophomore. I have also been > taking several extracurricular math classes with Squares & Cubes > <https://www.squaresandcubes.com/> on things like number theory, group > theory, discrete math, and linear algebra. In these classes we have > utilized Sage to explore mathematical patterns. For instance, in my > discrete math class, I used Sage's graph functionality to take a stab at > graph isomorphism, which eventually lead to a magazine article > <https://chalkdustmagazine.com/features/a-walk-on-the-random-side/> on > using random walks on graphs to solve graph isomorphism. > > During these various explorations, I realized that Sage was a very > powerful tool to explain and provide intuition for complex mathematical > concepts, however, (a) it is mainly used by those working in higher math, > and (b) there is a high barrier of entry to implement concepts (even ones > in lower math) in Sage. > > Thus, I wanted to contribute to Sage and *implement specific concepts > which I felt high school students like myself would find interesting*, > and use them for educational purposes (e.g. at my school). Two basic ideas > I thought of were: > > 1. *Random walks.* I think mathematics is often far more engaging with > a visual component (for instance, teaching graphing skills and different > types of equations through a Desmos art project), and I think when talking > about probabilities and randomness, an excellent visual representation of > stochastic processes is random walks, which are currently not implemented > in Sage. The other advantage of this is that random walks are often present > in other places such as physics (in Brownian motion). This could expand > into > 2. *Venn diagrams.* Venn diagrams are incredibly important; however, I > could not find any Sage implementations of Venn diagrams beyond simply > plotting intersecting circles. Having a more solid implementation could > provide a strong, visual intution for a variety of concepts, like basic set > theory, logical operators, probability, and even open the door for > Edwards-Venn diagrams! Such an implementation would utilize Sage's 2D > graphics (specifically the circle and text functions) as well as the > detailed Set implementation. > > > Several people who I contacted referred me to this group, and thus I am > wondering if anybody would be generous enough to (a) provide *thoughts on > the feasibility and usefulness* of such an endeavor, (b) provide some > *direction > or guidance* as to where to begin, and (c) offer any *potential avenues* > where this could be used. > > Until then, I will be beginning to work on any very simple bug fix I can > find to familiarize myself with developing in Sage. > > Thank you so much! > > Sincerely, > Tanmay Kulkarni > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/9a6e6925-87ce-4cdd-9d1f-c77d3ef986edn%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/9a6e6925-87ce-4cdd-9d1f-c77d3ef986edn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- F. Semih Dündar <[email protected]> -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAODtkKqq1n9kwMWe2RaySLTqoY7ry4T3%2BVmmBwGdWE%3DJBpgSRA%40mail.gmail.com.
