Ron's Transient Scraps
Zephyr Teachout: the http://ift.tt/1nSukGb

Zephyr Teachout: the http://ift.tt/1nSukGb

All the news that 6  http://ift.tt/1pEE2Bw

All the news that 6 http://ift.tt/1pEE2Bw

The Political Views  http://ift.tt/1q7wTZP

The Political Views http://ift.tt/1q7wTZP

Hot dogs http://ift.tt/1zYz1UK
Butterfly in my yard http://ift.tt/1rGi1UO

Butterfly in my yard http://ift.tt/1rGi1UO

Flowchart: Should Yo http://ift.tt/1rGi1UK

Flowchart: Should Yo http://ift.tt/1rGi1UK

Teacher Memes http://ift.tt/1rGi1UE

Teacher Memes http://ift.tt/1rGi1UE

Change in uninsured  http://ift.tt/1tUfW7o

Change in uninsured http://ift.tt/1tUfW7o

Self-selection and c http://ift.tt/1ktytEH

Self-selection and c http://ift.tt/1ktytEH

spring-of-mathematics:

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:

  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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

Images: How to Slice a Bagel into Two Linked Halves by George W. Hart - Cutting bagels into linked halves on Mathematica. - Interlocking Bagel Rings

Maybe, that’s one of the reasons why I love bagel :)

Teens in the last 20 http://ift.tt/XckPet

Teens in the last 20 http://ift.tt/XckPet

Actual outdoor sculp http://ift.tt/W32pwb

Actual outdoor sculp http://ift.tt/W32pwb

Oooh.  Super self-re http://ift.tt/1nejdpB

Oooh. Super self-re http://ift.tt/1nejdpB

And now you’re older http://ift.tt/1nejb0L

And now you’re older http://ift.tt/1nejb0L

Obamacare’s impact o http://ift.tt/1qnauoR

Obamacare’s impact o http://ift.tt/1qnauoR