I attended a presentation recently that included a discussion of the Fibonacci number sequence and golden spirals. We have discussed Fibonacci numbers and golden spirals here at Partial Ellipsis of the Sun before.
The Fibonacci number series begins as 0, 1, 1, 2, 5, 8, 13, 21, 34, 55, 89,144; each term is the sum of the previous two terms. The Golden Spiral is created using phi, the ratio of 1.6180. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities thus:
The illustrations in the presentation included spirals that looked like this:
Of course, Golden Spirals look like this:
No one else in the audience seemed bothered by equal spacing on the spiral; it drove me bonkers. Folks commented on how beautiful the illustration was; but it was wrong!
The Golden Spiral can be seen in the Milky Way:
And in storm patterns:
It can also be used in image composition:
I brought the spiral conundrum to the kindergartners who all saw immediately that the spiral had to grow so the chambered nautilus could grow, too.
From the mouths of babes. . .
Speaking of babes, a shout-out to my co-teacher who turned 60 on the 6th. The Babylonians considered 60 the most sacred number and a resetting of the odometer to zero in their base-60 number system. Happy sexagesimal reset, Mary!
Does it drive you bonkers when illustrations are wrong?
^^^Thanksgiving Square Chapel, Dallas, TX
Steph
Christmas Eve at Great Sand Dunes National Park and Preserve. It was an extraordinary day shared with a herd of 30 elk. See if you can find them.
Happy Sandy Holidays!
The Fibonacci number series begins as 0, 1, 1, 2, 5, 8, 13, 21, 34, 55, 89,144; each term is the sum of the previous two terms. The Golden Spiral is created using phi, the ratio of 1.6180. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities thus:
The illustrations in the presentation included spirals that looked like this:
Of course, Golden Spirals look like this:
No one else in the audience seemed bothered by equal spacing on the spiral; it drove me bonkers. Folks commented on how beautiful the illustration was; but it was wrong!
The Golden Spiral can be seen in the Milky Way:
And in storm patterns:
It can also be used in image composition:
I brought the spiral conundrum to the kindergartners who all saw immediately that the spiral had to grow so the chambered nautilus could grow, too.
From the mouths of babes. . .
Speaking of babes, a shout-out to my co-teacher who turned 60 on the 6th. The Babylonians considered 60 the most sacred number and a resetting of the odometer to zero in their base-60 number system. Happy sexagesimal reset, Mary!
Does it drive you bonkers when illustrations are wrong?
^^^Thanksgiving Square Chapel, Dallas, TX
Steph
Christmas Eve at Great Sand Dunes National Park and Preserve. It was an extraordinary day shared with a herd of 30 elk. See if you can find them.
Happy Sandy Holidays!
Speaking of Golden Fibbers.... And, speaking some more....
ReplyDeleteEw, just ew.
DeleteI don't need bad illustrations to drive me bonkers. I'm close enough to walk.
ReplyDelete;-)
DeletePasta comes in many shapes, including shells, but not chambered nautilus shells, as far as I know, and gnocchi aren't really shells. When pasta makers talk about the Golden Ratio, they're talking about how much water to how much pasta, which is altogether different.
ReplyDeleteWhen my wife first set up her private practice in Nutley, NJ, a heavily Italian-American community, her patients would sometime talk about their seasonal cooking, including making gavadeel, which we'd never hear of. On one trip to the Shop Rite, we heard over the PA system of a sale on gavadeel, avalable in a certain aisle. Hustled over there, but couldn't find it anywhere. Later, another announcement pinpointed it to the freezer at the end of the aisle. Which we found full of cavatelli. Doh! Sicilians!
Yeah, it was a bit of a stretch. I hate when folks fib about gnocchi, though.
DeleteCavatelli: little (sleepy) hollows. Deal away!
Over 600 pasta types and no chambered nautilus shells?
DeleteWhat a travesty:
https://pastafits.org/pasta-shapes/
And there are some pastas you just don't want to put in your mouth.
DeleteThey should've sponsored Season 1 of American Vandal.
DeleteFINALLY, an article that isn't filled with all sorts of science-y stuff. Mathematically, the ratio, 1.618(...) minus 1 = 0.618(...) which is the same as 1/1.618. But, for the sake of this blog, I refer you also to this video, which hints at some of the natural logic in that proportion.
ReplyDeleteIn school we used the term golden mean or golden section, but it's all the same thing. Architects have been using this proportional system for millennia: Greek Temples, Palladian Villas, and the modern architect Le Corbusier. There is some debate whether the early practitioners were consciously aware of these proportions, or whether they were just doing what looked nice.
Further reading can be found in the very important essay (at least for architects) The Mathematics of the Ideal Villa and other Essays written 70 years ago by Colin Rowe. Personal note, the last time I saw Colin was when I bumped into him at the Palazzo Massimo in Rome, which uses the golden mean in it's facade, particularly the spacing of the columns in the portico.
Colin has since passed to another golden section of the universe.
And of course I meant "golden mean in its facade..." Where is that dang copy editor?
DeleteThanks for the short and informative video and the links, eco. I have not gotten through much of the ideal villa paper, but it looks fascinating.
DeleteThe Palazzo Massimo looks most inviting.
Fear not if you can't make it through, Rowe's writing is pretty pedantic, and the topic is pretty specific.
DeleteMeanwhile, Jan can go bonkers, but let's hope he doesn't go batty. Though in this article the illustrations are beautiful.
I would not want the job of gluing tiny transmitters on the backs of bats. That really would drive me batty.
DeleteIt's like, Far Out, (wo)man!
ReplyDeleteOr a 4th note fight?
DeleteFa rout. . .
Just wanted to post an update here: after two weeks without, my senses of smell and taste seem to be coming back. A little intermittently, like a circuit with a broken wire, rather than gradually, as I'd expect, but I'll take it. Weird.
ReplyDeletejan, we always knew you’d pass the smell test.
DeleteSo that's your two scents worth?
DeleteYou nose it.
DeleteWow! Flowering plants may have appeared 50 million years earlier than we thought >>>
ReplyDeletehttps://www.zmescience.com/science/biology/flowering-plant-origin-04235/
Makes scents. Oh wait, already covered that.
DeleteEver notice that the French words for inhale/exhale are inspire/expire? Been on my mind for years.
Oui.
DeleteWhat is French anyway?
Spanish, but spoken in cursive.
OLD BAY/NEW BAE
ReplyDeleteIs that the baesis for a lawsuit?
DeleteBy Beyoncé?
DeleteA diatom wreath:
ReplyDeletehttps://epod.usra.edu/blog/2018/12/diatom-wreath.html
I added new images to the end of this post.
ReplyDeleteHappy holidays, PEOTSians All!
I guess the elk are considered essential federal employees?
DeleteWhoever herd ;-) of such a thing.
DeleteSome observations:
1. Two 20-something's were flying a drone not far from the elk, knowing the rangers were not working. I glared at them. They looked sheepish and landed the drone.
2. A deer along the Medano Pass Road licked a car all the way around for the salt.
3. Music - blaring, pot-smoking folks were so loud in the main dune parking lot we had to leave. The bathrooms were quite unpleasant.
4. A "LAW ENFORCEMENT" Park Ranger drove past us on the 4WD Medano Pass Road. There was only one other car out that far where orange cones blocked the road; uh oh.
5. The shadows are what make the Dunes so dramatic. Today, without sun they were rather flat, a bit livid-looking. Still wonderful, though.
We were surprised to see the park ranger in law enforcement out today. Wonder what was happening. . .
DeleteMy incomplete understanding is that they are able to keep the National Parks open because they have a separate budget for law enforcement/ safety rangers, but not rangers for visitor services. There was a shutdown a few years ago where there was no money for any kind of ranger, they had to completely close the parks.
DeleteUnfortunately the idiots will try to take advantage of the situation. How many elk did Big Bad Maizie hunt down for your Christmas dinner?
Maizie was in awe. We both were.
DeleteSo curious about the fellow I passed on the sandy 4WD road. Why was law enforcement after him in such a big hurry? He was a waver. Do wavers commit nefarious crimes in National Parks? And what was the alleged crime?!
Lady Cartographers
ReplyDeleteI found this obituary of Nancy Roman disappointing on several levels. In what sense was she the "mother" of the Hubble Space Telescope, which was adapted from the National Reconnaissance Office's KH-11 spy satellites that had been developed in previous decades? And why is that fact never mentioned? What exactly was her role the Hubble program? And how can someone named Roman be asked why she was taking math rather than Latin without a dope slap, or at least a snappy comeback?
ReplyDeleteYes, it is very disappointing.
DeleteThey could have, at least, made a Mother Hubble/Hubbard pun if they were bent on that tenuous Hubble angle.
The obit in the Post was slightly better - more Hubble background. I'm glad neither sunk so low as to play the Hubbard or Roman angles.
DeleteToo bad Hollywood doesn't make serious movies any more, there's a lot to be mined in her story.
Cubic Wombat Poop and More
ReplyDeleteVery weird watching Jeopardy tonight - dated contestant for about a year in high school.... long ago.
ReplyDeleteWow, I bet that was weird!
DeleteDrawdown: Refrigerant Management, Educating Girls, and More:
ReplyDeletehttps://www.vox.com/energy-and-environment/2017/5/10/15589038/top-100-solutions-climate-change-ranked
Jeffrey Dahmer's first snowman?
ReplyDeleteThough the orange color, primitiveness, being almost completely out of touch and the strange orbit not in line with much of anything else makes me think of another massive rock-headed snowflake....
It reminds me of mitosis.
DeleteShould you see a podiatrist?
DeleteIsn't this the opposite of mitosis? I suspect the agglomeration has astronomers (and spacey geologists) thrilled.
Ooh, chondrites in thin section:
ReplyDeletehttps://epod.usra.edu/blog/2019/01/encore-chondrite-thin-section.html
First, comet 67P/Churyumov-Gerasimenko. Now, Ultima Thule. Maybe everything out there in cold, deep space looks like a snowman?
ReplyDelete(Or, am I just being a dumbbell?)
DeleteHaha
DeletePerhaps we are all just lumps of mashed potatoes, or perhaps....
DeleteElectric spiders:
ReplyDeletehttps://www.theatlantic.com/science/archive/2018/07/the-electric-flight-of-spiders/564437/
I'd seen an article about that a few months ago. I chose not to share it with my office-mate, who has a real problem with spiders. Flying spiders might just push her over the edge.
DeleteI've always found animals (and plants) with superhuman senses -- geomagnetism, polarized light, UV or IR vision, etc -- interesting. Spiders that sense electric fields (like some fish) make my hair stand on end....
Maybe you saw that here?
DeleteHow prescient that I wrote "I suppose next you'll be telling us spiders use electricity to fly"
eco, I knew that topic looked familiar. . .
DeleteI think I first saw it in The Atlantic, but hoping to appear smart I linked to the Current Biology article, which does have a cool video.
DeleteIt took a good part of my elementary school years to master this technique, perhaps because Ididn't know about the rippling effect.
ReplyDeleteIs this why we have science research? Clearly the first testers did not know the right technique.
Band practice
DeleteOk, I do revel in the privacy and non-tracking at DuckDuckGo.com. But, today’s Google Doodle by a second grader who wants to be a paleontologist is fantastic. The dinosaur eating the blueberries right off the bush is inspired:
ReplyDeletehttps://www.usatoday.com/story/tech/news/2019/01/08/google-doodle-second-grader-creates-adorable-dinosaur-logo/2511750002/
I liked the stegosaurus floating from their bubble gum balloon - isn't that feasible if they burped a LOT of methane?
Deletelunchtime reading
ReplyDeleteHappy Blue Year!
ReplyDeleteNew post on “Am I Brilliant Blue? Lapis Lazuli Embedded in a 1000-Year-Old Woman’s Teeth” is now up.
LL-liking WW