… Y’see, now, y’see, I’m looking at this, thinking, squares fit together better than circles, so, say, if you wanted a box of donuts, a full box, you could probably fit more square donuts in than circle donuts if the circumference of the circle touched the each of the corners of the square donut.
So you might end up with more donuts.
But then I also think… Does the square or round donut have a greater donut volume? Is the number of donuts better than the entire donut mass as a whole?
A round donut with radius R1 occupies the same space as a square donut with side 2R1. If the center circle of a round donut has a radius R2 and the hole of a square donut has a side 2R2, then the area of a round donut is πR12 - πr22. The area of a square donut would be then 4R12 - 4R22. This doesn’t say much, but in general and throwing numbers, a full box of square donuts has more donut per donut than a full box of round donuts.
The interesting thing is knowing exactly how much more donut per donut we have. Assuming first a small center hole (R2 = R1/4) and replacing in the proper expressions, we have a 27,6% more donut in the square one (Round: 15πR12/16 ≃ 2,94R12, square: 15R12/4 = 3,75R12). Now, assuming a large center hole (R2 = 3R1/4) we have a 27,7% more donut in the square one (Round: 7πR12/16 ≃ 1,37R12, square: 7R12/4 = 1,75R12). This tells us that, approximately, we’ll have a 27% bigger donut if it’s square than if it’s round.
tl;dr: Square donuts have a 27% more donut per donut in the same space as a round one.
Thank you donut side of Tumblr.
GAME OF COMETS
"The red comet means one thing boy, dragons."
For centuries, comets were considered omens, usually bad omens. The appearance of a comet augured the death of a king or a coming catastrophe. The Battle of Hastings in 1066 famously coincided with an appearance by Halley’s Comet. For the English King Harold II, who died in the battle, it was a bad sign. For William the Conqueror, who went on to defeat Anglo-Saxon Britain, it was most definitely an auspicious phenomenon. It’s said that he declared the comet was a “wonderful sign from heaven.” Even more passionately, the monk-astrologer Eilmer of Malmesbury decried how Halley’s Comet kicked Anglo-Saxons in the ass:
"You’ve come, have you? … You’ve come, you source of tears to many mothers, you evil. I hate you! It is long since I saw you; but as I see you now you are much more terrible, for I see you brandishing the downfall of my country. I hate you!"
In the medieval fantasy world of Game of Thrones, it’s no different. When a red comet appears, everyone’s ready to project their feelings onto the crimson ice ball. But back in reality, do comets come in red?
Universe Today talked to astronomer Matthew Knight of the Lowell Observatory. The appropriately named Knight said a red comet wouldn’t be possible because the emissions are in the green and blue regions, usually from gases such as hydroxide and cyanide. But there is a close-to-red emission called “forbidden oxygen” in which atoms give off energy in between excited states. Knight continues:
The visible light from a comet comes from a combination of reflected solar continuum (sunlight reflecting off of dust grains) and cometary emission (neutral and/or ionized molecules of gas that emit photons at a particular wavelength). The sunlight reflecting off of dust grains basically looks like sunlight and since the Sun appears yellow/white, this component cannot look red.
A small caveat is that due to the physical properties of dust grains, comet dust often actually does “redden” sunlight slightly when measured with sensitive equipment. However, this reddening is at a very low level and is not enough to cause the reflected sunlight to appear a deep red like in Game of Thrones. The strongest comet emissions in the region where human eyes can see are in the blue and green regions.
For a comet to look like the red one observed in Game of Thrones, Knight says it would have to have a “strange composition” unknown to anything we know in our own star system: “In any event, the composition would be so anomalous that this comet would almost certainly have originated in another solar system. That would make comet scientists very interested in studying it!”
Explosive Surprise: Huge Volcanoes Shook Mercury for Billions of Years
Explosive volcanic eruptions apparently shaped Mercury’s surface for billions of years — a surprising finding, given that until recently scientists had thought the phenomenon was impossible on the sun-scorched planet.
This discovery could shed new light on the origins of Mercury, investigators added.
Amethyst Cast - Artigas, Uruguay
Amethyst crystals formed over a Calcite crystal, the Calcite is now gone leaving this hollow cast