\

Timid Thoughts & Vainglorious Musings

Ask me anything

Submit

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 :)

3,120 notes   /   reblog

What is it with me and short-haired cashiers?

1 note   /   reblog

sextradite:

ridge:

IM REALLY TIRED OF PARENTS THINKING THAT EVERYONE ON THE INTERNET IS A PREDATOR 

ikr wanna meet up and talk about it so where do you live?

(via soupery)

Game of Thrones Cast attends the panel and Q&A during Comic-Con International 2014 at San Diego Convention Center on July 25, 2014 in San Diego, California

(Source: stiles-stlinski, via stormofsnow)

8,844 notes   /   reblog

merriamwebsterdictionary:

reasons why winter is better than summer:

  • little to no insects (◕‿◕✿) 
  • sweaters all the time (◠△◠✿)
  • the air is nice and fresh smelling (◡‿◡✿)
  • sometimes it snows and you get out of school \(◕‿◕✿)/
  • snow is pretty (´・ω・`)
  • no pollen (▰˘◡˘▰) 
  • it gets darker faster so theres more nighttime and more time to look at the stars (ᅌᴗᅌ* )
  • everything is dead just the way i like it (⊙‿⊙✿)

(Source: puyopuyofever-remade, via thehorsemeatscandal)

Older →