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Maths Problem: Connect the towns solution (Motorway Problem)

singingbanana singingbanana·174 videos
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Uploaded on Jun 7, 2011

What is the minimum amount of road needed to connect these four towns together? Known as the Motorway Problem or Steiner Problem. An experimental solution.

With thanks to Scott Grandison of the University of East Anglia for all his help! And David and Neil of the workshop for making the props!

Reference: Problem solving with soap films: Part I, C Isenberg 1975 Phys. Educ. 10 452 http://iopscience.iop.org/0031-9120/1...

More information from wikipedia: http://en.wikipedia.org/wiki/Steiner_...

If you liked this, you'll also like "Slime Mold Grows Network Just Like Tokyo Rail System" http://www.wired.com/wiredscience/201...

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Uploader Comments (singingbanana)

  • Maurice D. Alexander

    Maurice D. Alexander 1 month ago

    The soap wants minimize tension, the minimized tension yields the minimized area of the soap 'walls' between the squares.

    What is the logic behind this in two dimensions?

    As in, considering there are infinite configurations - how would you prove this correct without the use of the soap that wants to minimize tension?

    ·

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  • singingbanana

    singingbanana 1 month ago

    Do you mean what is the theory and the maths? It's called Calculus of Variations.

    · 11

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    in reply to Maurice D. Alexander (Show the comment)

Top Comments

  • KarmaProstitute

    KarmaProstitute 2 months ago

    You're awesome ! Period. Exclamation mark ! 

    · 23

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  • Candoran2

    Candoran2 2 days ago

    It's called Calculus of Variation.

    ·

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    in reply to GelfandTransform (Show the comment)
  • Candoran2

    Candoran2 2 days ago

    With the 8 towns, you could leave one road out and it would be even smaller. By the way, in 3-dimensional environment, would the vertices there be the same as when you connect the center of mass of a tetrahedron to its vertices?

    ·

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  • iLuvHinata360

    iLuvHinata360 3 days ago

    the blow part at the end was "mind-blowing".

    ·

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  • GelfandTransform

    GelfandTransform 4 days ago

    Does anyone know of a reference in which the math of this problem's solution is shown?

    How about for higher dimensions? For instance, if you take the eight vertices of a cube as the points to be connected, what will the minimum solution look like? Maybe the projection onto one (or more or all) of the planes will correspond to the four-point plane solution.

    ·

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  • MrSebastify

    MrSebastify 1 week ago

    could you do like a video on how to - mathematically - prove/come to the solution? :D

    ·

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    in reply to singingbanana (Show the comment)
  • Matt Siegel

    Matt Siegel 1 week ago

    sweet, computers made of soap :D

    ·

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  • snemeis90

    snemeis90 2 weeks ago

    Damn, I was close. I thought about a shape like )-(

    A sort of bent H-shape.

    I had trouble figuring out how to calculate the total length.

    ·

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  • ongelvin

    ongelvin 2 weeks ago

    Mind. Blown.

    ·

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  • Sheng Lu

    Sheng Lu 2 weeks ago

    simply amazing!!!!!

    ·

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