An Illinois couple adopted baby Jennifer, who was born without legs. She loved to watch tumbling and idolized gymnast Dominique Moceanu. Jennifer’s adoptive parents wouldn’t let her give up and she actually became a high school tumbling champion in the state of Illinois. It turns out Jennifer and Dominique are biological sisters. Never Say You Can't: Jennifer Bricker Story - YouTube
And to complete the point, until you start getting to the really long polymers, all molecules are within a magnitude the same size. Therefore, while you’d think C[sub]4[/sub]H[sub]10[/sub] would be a lot bigger than H[sub]2[/sub], it’s pretty much the same size while holding five times the hydrogen atoms.
(1) Genesis Chapter 46 goes into excruciating detail to name the 70 descendants of Jacob who accompanied Jacob into Egypt or who were already there. Yet whenever you add up the subtotals, the arithmetic is off by 1. Faulty arithmetic by a scribe who found the list boring? Then why is the chapter carefully worded to create a logic puzzle whose solution implies a specific fact never explicitly stated?
[quote="D18, post:95, topic:851674"]
0! = 1.
[/QUOTE]
Since n!/n = (n-1)! even when n = 1, 0! = 1 isn't so interesting.
I think it's remarkable that
(2) (-½)! = √πI always liked math, wish I’d pursued it longer.
The negative sign before 1/2 is a typo, yes? And the square root of pi should be divided by 2?
So 0! = 1 and 1! = 1, and between them is less than 1. Interesting...I never considered non-integer factorials.Another contribution to the thread: if you’re like me, chopping onions causes your eyes to water profusely. I’ve tried wearing glasses, keeping mouth closed…what finally worked, though: put the whole onions in the freezer for 10-15 minutes before you begin.
Substitute n = ½ into the factorial rule (n-1)!·n = n! and, starting with the formula I gave for (-½)!, you’ll get (½)! = ½·√π
So, yes, if you make BOTH the corrections you mention you get a correct formula for (½)!. Make NEITHER correction and retain the correct formula given for (-½)!
Instead of writing these as factorials of fractions, they are often written as Gamma (Γ) function; they were devised by two of the greatest Swiss mathematicians from the 18th century.
I think it’s selling Euler a bit short to call him “one of the greatest Swiss mathematicians of the 18th century”. He’s got a reasonable claim to the title of “greatest mathematician in history”.
And you can’t leave us hanging on the Genesis logic puzzle. If you were waiting for someone to ask, well, I’m asking.
I’ll have to reflect on all that.
This guy?
During a walk today (permitted exercise!) I was reminded of the time when I got so perplexed by seeing things marked “Pillow Mound” on an OS map that I gave in and looked them up (the wiki)
Here’s an aerial view (google earth) of a bunch of them.
We walked past a couple today, but then they really are all over the place round these parts.
j
Mesa Verde in Coloradoprobably has it beat. But I guess it depends if you call a cliff dwelling a building. It’s impressive in any case.
When I was growing up in Portland, there was a columnist in the daily Oregon Journal, Dick Fagen, who called his column “Mill Ends.” He could see that little circle of concrete from his office window, and he established and named that park unofficially, until it was made official in 1976, after his death.
I was going to quote this fun fact that was posted on Facebook 3 days ago: San Francisco (where I now live) was incorporated on April 15, 1850, and that’s why the telephone area code is 415.
I was the tiniest bit suspicious, so I checked. Alas, both parts of that are made up, so I got nuthin’.
A founding member of Sha-na-na went on to become a linguistics expert:
Founding member Robert Leonard is a professor of linguistics at Hofstra University. He had an appearance as a qualified expert in linguistics for the murder case of Charlene Hummert in the episode “A Tight Leash” of the TV medical detectives series Forensic Files in 2004,[16][17] as well as for the Tennessee “Facebook Murders” on the Investigation Discovery crime show Too Pretty to Live in 2016.[18][19]
Wombats have the largest brains of any marsupial.
I’m confused, so I checked, too.
Yes, SF was incorporated on that date. San Francisco - Wikipedia
The area code for SF is and has always been 415. But that area code originally covered a much larger area, so only reliable documentation could justify the connection with the date. Area codes 415 and 628 - Wikipedia
I’d put Euler 4th on the all-time list myself. 
The peculiar phrasing was because Euler’s friend Daniel Bernoulli may also have been involved in the discovery of the Gamma function.
The Genesis chapter has long lists of people; this (intentionally?) obscures the puzzle and the associated Mystery person. Here’s a summary of Genesis Chapter 46 intended to present the Logic Puzzle, though it offers little in the way of helpful hints. I assume you don’t want me to show “the Spoiler” here, but I’ll give these further hints:
[ul]
[li] Jacob himself is not considered to be ‘of the House of Jacob.’[/li][li] The list of Leah’s descendants (verses 8-15) names 32 living persons (not counting Israel/Jacob and Leah), but see “all the souls of his sons and his daughters [which Leah bare] were thirty and three” in verse 15.[/li][li] The mysterious 70th person (at least in Pratt’s solution to the puzzle) is explicitly named in the Chapter.[/li][li] Verses 26-27 highlight the arithmetical discrepancy, and have a particular structure that a cunning logic-puzzle designer might use.[/li][/ul]
Me too, so I contribute the five most relevant numbers and four mathematical operations all together in a single equation:
1 + e^i*π = 0
That was Euler too, of course.
Concerning the onions, few people know that wearing hard, gas permeable contact lenses completely prevents crying while chopping them (the onions, not the lenses). And they do not know because people like me who wear them do not usually tell, otherwise we would be assigned that tedious task every time onion chopping came up (and your hands still stink afterwards) 
There you have yet another reason not to perform LASIK.
I swear I looked up and down on that page yesterday and didn’t see anything about incorporation. I didn’t think to do a word search though. Now I have to go back and apologize to someone.
I read that NYC got the 212 area code because it was very easy to dial on a rotary phone. Chicago got 312 . The idea was the biggest cities got the lowest number area codes.
I tried to post this in the “Animal Surnames” thread, but it got ate.
Maverick - the word that now means a non-conformist, also means an unbranded calf or horse - and that came from a man named Silas Maverick who was bad about branding his calves (Merriam-Webster says he was a lawyer who accepted the calves as payment, then didn’t get around to branding them)
And according to etymonline, the meaning of “non-conformist” doesn’t derive from the unbranded calf meaning, but from the Silas Maverick’s grandson, who was “famous for his liberal independent streak” maverick | Search Online Etymology Dictionary
And to attest to the second half of the thread title… I read this first in one of those Time-Life series books, in this case the one about the old west. And I read this story because the book was on a table at a used book store, and I just randomly opened it (or maybe it was randomly open) to the page with this story on it. And that is the sum total of anything I’ve read from that particular Time-Life series.
Brevard County, Florida, the location of Cape Canaveral - where the space shuttles used to launch from - has the area code 321; I assume that “blast off” comes next.
…
Abe Lincoln’s birth mother was named Nancy Hanks. Tom (the well known Covid survivor) is a descendant of that same family.
…
Franklin Pierce was the 14th American President. Barbara Bush, wife of one president and mother of another, had the maiden name Pierce, and is a descendant of Franklin’s family.
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Singer Carly Simon’s dad was the Simon in Simon and Schuster, the publishing company.
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Winston Churchill was the name of a famous American author before it was known to be the name of an English politician.
(I realize that some of these probably aren’t all that obscure anymore, but they are trivia nonetheless!)