On Sharing a Birthday

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On Sharing a Birthday

Something strange happened to me, once, on January 12, in a year in the early 1990s. Until that day, I knew of no one who shared the same birthday as myself. Then, that day, I happened to flip on my car radio, which was already tuned to a news/talk radio station. I was completely stunned by what happened next, for I had accidentally stumbled upon The Rush Limbaugh Show on his birthday — and mine. I learned this almost immediately, for one of Limbaugh’s callers said, right after I turned the radio on, “Hi, Rush! Happy birthday dittoes!”

Limbaugh laughed, and thanked the caller. I screamed, and then I yelled, “Noooooo! I can’t have the same birthday as Rush Limbaugh!” However, like it or not, I had to admit that this coincidence was, indeed, true. Also, since Limbaugh is older than I am, I also had to face up to the fact that he had this birthday first.

I wanted to have someone else to know I shared a birthday with — someone I could respect — so I did some research to find other people who also shared the same birthday as myself. In those days, of glacially-slow dial-up Internet with much, much less of value to be found there, this meant actually going to a physical library, looking in actual, bound-paper books (how primitive, right?), and spending a few hours to do what can now be done, with Google and Wikipedia, in seconds. I learned, in those hours, that I also share the birthday of January 12 with none other than John Hancock, the first person to sign the Declaration of Independence, according to the old-style system for the date of his birth. (The difference between old- and new-style dates is caused by the discrepancies between the Julian and Gregorian calendars.) Given that the primary author of that document was my all-time favorite president, Thomas Jefferson, that was something of which I could be proud.

In later years, I learned that Wikipedeans (a group to which I belong) have constructed pages there where anyone can quickly and easily learn with whom they share a birthday. The one for my birthday is here: http://en.wikipedia.org/wiki/January_12. By looking at the corresponding page for your own birthday, you, too, can find out whom you share a birthday. No matter what day that is, you’re quite likely to find, as I did, both people you like and dislike. After all, there are only 366 birthdays to go around, so sharing birthdays with famous (and infamous) people is inevitable for us all.

Obedience Is Not a Virtue

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Obedience Is Not a Virtue

No brilliant discovery, nor invention, was ever made by those who compulsively follow rules, demonstrate immense respect for authority, and make a habit of unquestioning obedience.

Rhombic Triacontahedron Featuring Octadecagonal Designs On Its Faces

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Rhombic Triacontahedron Featuring Octadecagonal Designs On Its Faces

The octagonal design on each face appears in the last post here, and was made using both Geometer’s Sketchpad and MS-Paint. After cropping this image, I projected it onto the faces of this polyhedron, the rhombic triacontahedron, using Stella 4d, a program you can try for yourself at http://www.software3d.com/php.

An Octadecagon, with Its Circumscribed Circle, and the Lines Containing All of Its Sides and Diagonals

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An Octadecagon, with Its Circumscribed Circle, and the Lines Containing All of Its Sides and Diagonals

Five

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Five

A Tessellation of Regular Polygons for the New Year MMXIV

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A Quasi-Regular Tessellation for the New Year MMXIV

All of the polygons in this tessellation are regular. There are only three regular tessellations, and they use, respectively, equilateral triangles, squares, and regular hexagons to tile a plane. There is also a set of eight semi-regular (or Archimedean) tessellations, which you may see here. Archimedean tessellations include more than one type of polygon, but they are vertex-transitive, meaning that each vertex has the same set of polygons surrounding it.

This is a tessellation of regular polygons, but it lacks vertex-transitivity, so it cannot be called a semi-regular (or Archimedean) tessellation. In other words, in this tessellation, there is more than one type of vertex.

There are many such tessellations with an indefinitely repeating pattern. Has this particular one been seen before? I do not know the answer to this question — but if you do, please let me know, in a comment.