6/28: So Much More Than Tau Day, It's a Perfect Day

      June 28th as Tau Day (pi x 2) is only part of the story of today's date. The digits in 6/28 (or 28/6, if you will, mate) are made up of two perfect numbers. A perfect number is a number that is the sum of its factors besides itself, and 6 (1+2+3) and 28 (1+2+4+7+14) are the first two perfect numbers. 

      Today is also my twin brothers' birthday. This morning, I also found out that my mom picked today, the perfect day, for inducing their birth! (It is also her best friend's birthday.)

     The next two perfect numbers are 496 and 8,128.

     

      The relationship between Mersenne prime numbers and perfect numbers is seen below:

      A Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number that can be written in the form Mersenne number = 2n − 1 for some integer n. They are named after Marin Mersenne, a Frenchman who studied them in the early 17th century. The first four Mersenne primes are 3, 7, 31, and 127 (although some of Mersenne's primes were proven later to be incorrect).

      As of May 2017, the largest known prime number is 274,207,281 − 1, a number with 22,338,618 digits. It was found in 2016 by the Great Internet Mersenne Prime Search (GIMPS-ha!). 

        Primes, GIMPS, perfection, oh my!

       Happy Birthday and have a luminescent trip around the sun, bros. Hope you had a parfait day!



Hope you've all had a perfect day, or at least a few perfect moments,
Steph

     5000 new neighbors moved into our backyard yesterday!

       

Cherry Blossom Stones : I Knew I Muscovite Away

     Cherry blossom stones (or "pinite") are a complicated group of six cordeirite crystals surrounding a central indialite crystal which have all then been replaced by muscovite in a second metamorphic event. I knew I muscovite about them after reading about them for the first time today.

      The structure of the stones is shown in this illustration (please forgive the 'intergorth' typo:

     The dumbbell structure including the central indialite crystal creates these intriguing stones which are not fossils:

      The type locality is near Kyoto, Japan, of all perfect prefecture places. And these stones are found in a hornfels (metamorphosed shale or mudstone) matrix. 

     So much change in temperature and pressure in those metamorphic rocks to create these delicate hexagonal structures! The end result are muscovite replacement crystals of these cordeirite-indialite crystals all on the hornfels rock.

        Chemically, indialite is a magnesium aluminosilicate mineral (Mg2Al4Si5O18).  Cordierite is an iron magnesium aluminosilicate mineral ((Fe,Mg)2Al4Si5O18).

      
      Have you heard of cherry blossom stones before? Does the complex interrelationship of the host rock, original crystal structure of two different minerals then replaced by another mineral in a hexagonal structure make you say "Wow?!"

Whoa. Wow,

Steph

New canine mountain friends on a perfect Colorado Day:

        We said our Colorado au revoirs this weekend. . . ZOË is Addis Ababa bound, home-made injera sourdough flat bread in hand ;-). A most excellent adventure until September, 2017; Colorado peeps will miss you! Excited to hear about your grand adventure!