Two Excellent Mathematical Websites

I usually only post my own work here, but today I’m giving a shout-out to the websites of a German friend of mine named Tadeusz E. Doroziński. He made this snub polyhedron with 362 faces, which I’m posting here as a sample of his work. All of its edges are of equal length. Like me, he uses Stella 4d: Polyhedron Navigator frequently (available here), and he used that program to create this polyhedron. 

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His two geometry-focused and polyhedron-filled websites, https://geometryka.wordpress.com/ and http://www.3doro.de/, contain much more, including some mathematics which flies right over my head, as the saying goes. If you like the image above, or you are a fan of my own blog, I strongly recommend following the links above to check out his work. Every time I visit either of his websites, I always find something amazing.

Bible Hub: A Website Review

http://biblehub.com/

bible hub

Whether one is a Christian, or not, we should all be able to agree that the Bible is an important book, and that greater understanding of it will benefit anyone who lives on this planet. There are, after all, well over a billion people, alive today, living in families which try to use the Bible as a guidebook for life. (As an aside: is it also true that anyone on earth can benefit from improving their understanding of the Qur’an? Of course it is — and for exactly the same reason.)

Before today, I had never encountered a website which serves that purpose — greater understanding of this important book we call the Bible — with the purity of Bible Hub. I found it by accident, while discussing, with my wife, the original languages in which the Bible was written: Hebrew for the Old Testament, and, in the New Testament, an ancient form of Greek — plus one important sentence (depicted as the last pre-death-and-resurrection words spoken by Jesus) in Aramaic. The New Testament was not written for an audience which understood Aramaic, so the books of the Bible which include this sentence (Matthew and Mark), as originally written (as far as we can tell), follow the Aramaic words of this sentence with a translation into the same form of Greek (Koine, or the ancient Greek of the common people, as opposed to the ruling class) in which the rest of the New Testament is written. The influence of Greek culture (which could have spread along with the Greek language) could only have affected the New Testament, not the Old Testament, for historical reasons. The two of us were discussing the possibility that the absence, then presence, of a Greek influence might help explain why the Old and New Testaments are so radically different from each other. For quite some time, though, I became sidetracked by my inability to remember the last words of Jesus on the cross, in Aramaic, and I decided to investigate that topic more closely.

I do not read Greek, so I have read the words in this important New Testament sentence (“My God, My God, why have you forsaken me?”) only in English translations of the Bible. I simply used Google to do a search for this sentence — and that’s how I found Bible Hub.

On the two pages at this website related to the verses I was researching, the first thing I found was an amazing variety of English translations of each verse, clearly labeled, including many translations of which I was previously unaware. Navigating to other languages is easy, at the upper right. Below the numerous English translations, there is commentary, but it is clearly labeled as such, so that no one will confuse the commentary with the various translations of the verses in question. If one wants to read sermons related to a given verse, there is an easy-to-find link provided for that purpose, but it is easier, of course, to not click on a hyperlink than it is to click on it.

My favorite feature of this website, by far, is that I was able to get the information I wanted quickly, without anything at all telling me how to interpret what I read. At Bible Hub, the default format is to let readers interpret the various parts of the Bible for themselves. For that reason, in addition to other features described above, I give this website an A+ grade.

Weaving Silk Online

thing

The image above took very little time to make, online, at this website. The user interface there allows a large degree of control over the shapes and colors used in the images one produces. I didn’t notice a “save image” button, but that’s what screenshots are for, right?