My favorite equation!
I just learned that this blog-hosting site (WordPress.com) has added LaTeX functionality to its text features. So in honor of God’s Sabbath, I thought that I would close today before I drop off to sleep (which may have already happened without my knowledge, actually) by paying humble homage to His creation by posting one of it’s most elegant (IMHO) features:
[Hopefully your browser is able to display that. Less cleanly, it should say e ^ (i π) + 1 = 0, where "^" indicates "raised to the power of".]
When I learned of this great truth I was giddy, and it has been my favorite equation ever since. My wife made it a part of the design of my “groom’s cake” at our wedding (which was lovingly designed as a teacher’s chalkboard, with the equation spelled out in white icing “chalk”). For me, it is one of the brightest, golden bricks in the wall of evidence that mathematical concepts are not invented by men, but instead are designed by God and merely discovered & explored by men. The mathematical symbols we use are simply the language we have devised to explain the mathematical truths we have discovered.
I feel another series of geeky posts in the works… I know that many mathematicians recognize the inherent beauty of this equation (Jerry P. King uses it to illustrate his definition of beauty in mathematics in The Art of Mathematics), but most others would have no idea what’s so special about it. Perhaps next week I will try to explain. Or, perhaps after I have gotten some sleep this will seem like a bad idea. I think I will let my pillow decide. Good night, Gracie, and I hope everyone has a wonderful and meaningful Sabbath.
Want to know what MY favorite number (with all its associated equations and geometric relationships) is? Phi, the Golden Ratio (1 + 5^1/2)/2 or 1.618033989… There have been a good number of interesting books published about this number, at least two by Dover Books; a third is called THE GOLDEN RATIO: THE STORY OF PHI, THE WORLD’S MOST ASTONISHING NUMBER by Mario Livio (Broadway Books, 2002). I lost my Dover books while moving out here, but I bought Dr. Livio’s book in the last couple of years. So if you can squeeze it in among all else, I recommend that you do. You won’t regret it (although your family, who sees little enough of you as it is, just might).
At this writing I have yet to see your latest broadcast, but plan to do so this morning and look forward to it. *Shabbat shalom `alayikh ve`al khol mishpatekha* (Sabbath peace upon you and all your family)!
Sorry to chime in again, but if you go on my blog you will see a couple of entries which feature a graphic of the Ark of the Covenant with the biblical Hebrew equivalent of “The Living Church of God” (*Qehal ha-Elohim ha-Chay*) superimposed on it. The proportions of the “flag” (leaving aside the buttonized border) are a very close approximation of the Golden Rectangle (1:1.618033989…). One entry that features this “Covenant flag” is “Why I’m not a Messianic Jew”. I’m forgetting the title of the later one that does also. (However, the same “flag” is now one of the featured photos on my front page.)
It may be that your favorite equation is somehow closely related to phi. So many other things are, often in unexpected ways — including fractals and natural logarithms. Maybe Dr. Livio’s book will point you in a direction that leads to a connection. (Too bad my browser — or my firewall — won’t let me see your graphic.)