odditudes-and-weirdities

On this date in 1924 a meeting of the American Astronomical Society began that presented conclusive evidence that the Andromeda Galaxy is separate from our own Milky Way Galaxy . For the first time, we could be certain that our universe consisted of galaxies separate from one another. (For the record, this idea had been kicking around for a couple hundred years.) This was primarily the work of Edwin Hubble , who used the Hooker Telescope to determine the distance from us of Cepheid variable stars  within Andromeda, convincing the astronomy community that they were way outside what we'd consider to be the Milky Way stars. Today we know there are a lot more galaxies than Andromeda, though exactly how many are out there is still a work in progress. A few years ago the estimate was around 2 trillion, but that's been revised downward to more like 200 billion. So take some time today to think about these giant gravitationally connected groups of stars and other matter. Hubble ESA

Happy Transistor Day! On this date in 1947 the point-contact transistor , the first transistor, was demonstrated at AT&T Bell Laboratories by  John Bardeen ,  William Shockley ,  and  Walter Brattain . Nine years later they would jointly receive the Nobel Prize in Physics for this work. Transistors went on to revolutionize the field of electronics. By Mister rf - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php? curid=80486830 Additional transistor history is here .

Happy Pronic Numbers Day! Pronic numbers (aka oblong numbers aka heteromecic numbers aka rectangular numbers) are the numbers obtained by multiplying consecutive non-negative integers together. The numbers start as: 0 X 1 = 0 1 X 2 = 2 2 X 3 = 6 3 X 4 = 12 4 X 5 = 20 It doesn't seem like pronic numbers are especially important, but they are old . It's believed that 6th century BC Pythagoreans knew about these numbers. The last 2 consecutive pronic numbers that form a date are 12/20, or December 20, which is why they're celebrated today.

Happy Abundant Numbers Day! What are abundant numbers  (aka excessive numbers)? They are related to the concept of perfect numbers , which are the numbers where the sum of the proper divisors is equal to 2 times the number itself. Abundant numbers are where the sum of the proper divisors is greater than the number. (The remainder, numbers where the sum of the proper divisors is less than the number, are called deficient numbers .) Here is the start of the set of abundant numbers. Every natural number is either perfect, abundant, or deficient. Here's the arithmetic that determines some of the early ones. We celebrate Abundant Numbers Day today because 12 and 18 are the 2 largest consecutive abundant numbers that form a date: 12/18 or December 18.

Happy Composite Numbers Day! Composite numbers are sort of like the complement of the prime numbers (ignoring 1, which is neither), and each of them can be expressed as two or more prime numbers. For example, 12 = 2 X 2 X 3 (2 and 3 are primes) so it is composite, and 35 = 5 X 7 (5 and 7 are primes) so it is composite. Every positive integer greater than 1 is going to be either a prime number or a composite number. A subset of the composite numbers, the semiprime numbers , are the driving force behind  public key cryptography  Other interesting subsets of the composite numbers are the sphenic numbers and the powerful numbers . December 14 was chosen for Composite Numbers Day since they are the largest consecutive composite numbers to form a date: 12/14.