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 isn’t art-related, but this is EXTREMELY SERIOUS IF YOU LIVE IN THE US. The following message is pasted from Reddit user DrDreamtime. I did not write this, but it
contains all the most important information you should know. It should be spread as far and wide as possible.
those that do not know or understand what net neutrality is and would
rather see a video instead of a LOT of text, here is a good video by John Oliver on Net Neutrality.
Text RESIST to 50409
to get help from RESIST Bot. It helps you find your reps, write letters
to them, and sends them faxes FOR FREE. Everyone who cares about Net
Neutrality should take 5 minutes to write to your representatives, once a
week (or a day). Be heard.
The harder, but still very easy way:
Step 1: Find out who your Representative and Senator is/are.
FaxZero has a system set up allowing you to fax your Representatives and Senators
for free! (Faxes are good if you can’t get through on the phone lines,
or just if you want congressional staffers to listen to fax machine
noises until Net Neutrality is safe.)
Step 3: Call, write, or fax to express your feelings on this.
lot of people are nervous about calling their elected officials for the
first time, maybe you don’t know what to say, or how to say it, or even
who you’ll be talking to, so here’s what you’ll need to know.
a 75% chance your call will be answered by a Secretary who is
specifically there to listen to your concerns, there’s a 25% chance your
call will be bumped into a voicemail box which is specifically there to
listen to your concerns, there is a ~0% chance you’ll find yourself on
the phone with your Senator or Representative.
You may be asked for your name and address or zip code, it’s okay not to tell them if you don’t want to, but the information is useful for your elected officials. I usually just give my first name, zip code, and the name of my town.
worry about a script, don’t worry about being eloquent, you’re not
writing Shakespeare here, you’re a concerned citizen voicing their
frustrations, fears, and hopes. “I’m really scared of Ajit Pai’s plans
to roll back net neutrality, a free and open internet is important to me
because [Your reason here. Some suggestions: An open internet is
important to democracy/I worry what Donald Trump might do with more
power/Cable bills are already too high/etc.]. Please tell [Senator or
Representative] that I support a free and open internet, I support Net
Neutrality, and I vote.” The only hard and
fast rule is that you need to be polite; these folks are getting dozens,
if not hundreds of calls a day, they don’t need you bitching and
swearing at them for something they have no control over. Be passionate,
but be polite.
Reminder: Only call YOUR OWN elected officials!
Calling Mitch McConnell from sunny Florida won’t do anyone any good,
and might actually harm the cause. Only call your own elected officials,