Mathematically Correct Breakfast – How to Slice a Bagel into Two Linked Halves. If a torus is cut by a Möbius strip it will split up into to interlocking rings.
It is not hard to cut a bagel into two equal halves which are linked like two links of a chain. Figure 1:
To start, you must visualize four key points. Center the bagel at the origin, circling the Z axis. A is the highest point above the +X axis. B is where the +Y axis enters the bagel. C is the lowest point below the -X axis. D is where the -Y axis exits the bagel.
These sharpie markings on the bagel are just to help visualize the geometry and the points. You don’t need to actually write on the bagel to cut it properly.
The line ABCDA, which goes smoothly through all four key points, is the cut line. As it goes 360 degrees around the Z axis, it also goes 360 degrees around the bagel.
The red line is like the black line but is rotated 180 degrees (around Z or through the hole). An ideal knife could enter on the black line and come out exactly opposite, on the red line. But in practice, it is easier to cut in halfway on both the black line and the red line. The cutting surface is a two-twist Mobius strip; it has two sides, one for each half.
After being cut, the two halves can be moved but are still linked together, each passing through the hole of the other.
It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area. Topology problem: Modify the cut so the cutting surface is a one-twist Mobius strip. (You can still get cream cheese into the cut, but it doesn’t separate into two parts). See more at:Mathematically Correct Breakfast: How to Slice a Bagel into Two Linked Halves by George W. Hart.
This drove me crazy for a while, because I can do it- but I didn’t know what it was and I couldn’t figure out how to describe the rumbling sound in my ears. It usually happens when I shut my eyes super tight. Glad to see that I’m not alone, and that there’s a good explanation of what it is!
can everyone not do this??? i thought that hearing a rumbling static noise from the muscles in your ears when you squeezed your face shut really hard was universal
Idk if I can watch this Toys That Made Us documentary on Barbie because they’re constantly saying, “this had never been done before!” and every time I start screaming at the inaccuracy because Barbie was not the first extremely popular plastic fashion doll with boobs in the 1950s, ok, you had Alexander’s Cissy and Cissette dolls, Ideal’s Miss Revlon doll, Vogue’s Jill doll, Horsman’s Cindy doll, American Character’s Sweet Sue doll, as well as a bunch of dolls from smaller toy companies (not to mention the knockoffs). And they aaaaall tried to make money off the clothes and accessories, ok, Barbie was not the first to follow this business model. Literally there were so many dolls with boobs at Toy Fair by 1959, don’t make me get my vintage catalogs out
so what do you believe was Barbie’s actual additional value? Because I mean… I guess she *had* to stand out in some way to be propelled to global success like it eventually happened
Short answer – I think it was the clothes & accessories, the marketing, and the rise of postwar consumerism.
Long answer – I want to preface this by saying that my area of expertise in dolls is almost exclusively pre-Barbie. Like, my obsession goes from about 1932 to 1962, with an emphasis on the postwar period in America, so I know a liiittle bit about Barbie, but I am Not a Barbie collector.
Leo Lech is suing the police in Greenwood, Colorado for storming his house with a 50-person SWAT team because they mistakenly believed that a man who ran into his house (whom Lech didn’t know) had shoplifted a shirt and two belts from Walmart; the police engaged in a 19-hour standoff that led to the near-total destruction of Lech’s house due to the use of “calculated destruction,” a tactic through which explosives are detonated through the house, room by room, to isolate the suspect.
HOLLISTER, CA—Longing for the days when people understood the true meaning of the holiday, area man Steve Rocha told reporters Monday that he remembers a less politically correct time when Christmas was about honoring the glory of Saturn. “It was the one time a year when families would gather round the altar and sacrifice a suckling pig to the god who ruled in the Golden Age, but nowadays you have to act like you’re ashamed of that,” said 41-year-old Rocha, adding that people used to be allowed to openly celebrate the agricultural deity with a sumptuous public banquet and copious amounts of gambling and debauchery without being accused of some sort of religious intolerance. “You can’t even say io Saturnalia anymore without the PC police biting your head off. Boy, the days when you could spend Christmas serving your slaves as if they were your masters in an evening of fun role-reversal are long, long gone, I’m afraid.” At press time, Rocha was lamenting the fact that the holiday cups at Starbucks had not a single traditional image of Saturn devouring his own newborn children.
It’s scary – Bell, Cineplex, Shaw, and Rogers are trying to censor the internet and force the end of net neutrality in Canada. And worse, they’re trying to do it behind closed doors.
These 4 companies, led by Bell, are pushing to create an internet “blacklist” of certain websites that all internet service providers in Canada would legally have to block. They know this outrageous proposal would never pass, so first, they tried to sneak it into NAFTA negotiations – and now Bell is expected to introduce its proposal to Canada’s telecom regulator TOMORROW.
Critics are calling this move “unprecedented” and dangerous. If these companies get their way, this internet blacklist would have absolutely zero oversight in the courts. We need to stop this urgently.