July 30 is the 211th day of the year; as well as Sweetmorn, Confusion 65, 3184 YOLD to discordians.

That said, I'm going to skip my usual intro and kick around the number 30 a bit. It is, of course, the product of the first 3 primes, 2, 3, and 5, and if that doesn't get your blood stirring, then you're pretty much normal in that respect.

Thirty is, however, an important piece of something, to wit, a circle. List the products of 30 and you get:
0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360, mapping, among other things, the cardinal points on a compass and the points of intersection of a unit circle centered on the origin with an orthagonal set of axes. Oh yeah, Big Whoop. Ok so poke aroung a bit more.

The first 3 non-zero products above, 30, 60, and 90, form a pretty spiffy right triangle, one that is standard issue for classical draftsmen. Fun fact: the hypoteneuse is twice the length of the shortest side (adjacent to the 60 degree angle). If we stand it upon the short side, which thus becomes the base, the remaining side is now the height, and pythagoras tells us that it is the square root of the square of the hypoteneuse ((2x)²) minus the square of the base (x²). Zo, (4x² minus x²)^1/2 which comes to x times the square root of 3, or 3^1/2x.

So, with geometry over, how 'bout trig? Because they are the opposing non-ninety degree angles, the tangent of 60 is the cotangent of 30 and vice versa. So, replace x with 1 and opposite over adjacent for the 60 is square root of 3, the tangent of 60 and cotangent of 30. For the 30, opposite over adjacent is 1/3^1/2, tangent 30 and cotangent 60. What's left? The sine is opposite over hypoteneuse, which is 1/2 for the 30 and (square root of 3)/2 for the 60. The cosine is adjacent over the hypoteneuse which is (square root of 3)/2 for the 30 and, you guessed it, 1/2 for the 60.

Twenty years of schooling and they put you on the day shift, look out kid, ...

On this day in:

0762 – Baghdad was founded and rapidly became "a significant cultural, commercial, and intellectual center for the Islamic world" per the wikipedia.

1729 – Baltimore was founded and rapidly became a major port for the tobacco trade and somehwat later a marketplace for such diverse products as sugar and slaves.

1956 – The U.S. Congress, abetted by President Dwight D. Eisenhower, criminally conspired to make In God we trust the U.S. national motto, because every nation needs a motto and because we had to counter godless communism. This was an outgrowth and continuatin of a previous secret policy widely independently adopted by a lot of the populace as well as the government that there was a desperate need to counter the fact that some Russians and some Communists were capable of rational thought, thus all the disdain and scorn for "eggheads", "thinkers" and intellectuals from the fifties to this very day.

1962 – The Trans-Canada Highway officially opened.

1965 – LBJ signed the Social Security Act of 1965 establishing Medicare and Medicaid. A giant victory for both godless communism and rational thought which was greatly resisted at the time and which has been under attack ever since.

1975 – Jimmy Hoffa vanished, permanently, forever. Some hypothesize that this may have been the rapture, at long last, and that he was the only qualifying individual.

Born this day in:

1818 – Emily Bronte, a novelist and poet, who wrote Wuthering Heights

1857 – Thorstein Veblen, an economist and sociologist. He introduced the ideas of conspicuous consumption and conspicuous leisure which he decried. An influential progressive during the so-called progressive era, he was quite critical of capitalism and hence is pretty much ignored and untaught today.

1881 – Smedley Butler, a US general and two time Medal of Honor winner who wrote and spoke critically of war and capitalism, including the 1935 booklet "War is a Racket". War is a Racket is available on amazon and here: http://feralhouse.com/war-is-a-racket/ and free from the archive http://feralhouse.com/war-is-a-racket/. But, it was both a speech and a booklet, which was later revised, and may run from 10 pages to 120. Butler also exposed the Business Plot.

1936 – Buddy Guy, a singer, songwriter, and guitarist who also played bass on very rare occasions.

1941 – Paul Anka, a singer, songwriter and actor

1946 – Jeffrey (Hammond) Hammond, a bass player who played with Jethro Tull and who also invented the claghorn

Died this day in:

2003 – Sam Phillips, a record producer and the founder of Sun Records. The list of artists he recorded and published is simply amazing, and should be moreso when one realizes that, for whatever reasons, he passed a lot of recordings on over to Chess. I'm trying to conserve readers' bandwith, or I could easily blow up the intertubes by simply playing one or two recordings each of his best known performers.

Holidays, Holy Days, Festivals, Feast Days and such:
National Cheesecake Day
World Snorkling Day
Paperback Book Day
International Day of Friendship

picture: "Friendship in Snow" from the Salem Maritime National Historic Site, public domain

It's an open thread, so do your thing