Tree Gaps and Orchard Problems - Numberphile

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  • Published on Jan 26, 2018

  • Get 10% off at Squarespace: https://www.squarespace.com/numberphile This feature features Ben Sparks... More links & stuff in full description below ↓↓↓ Ben Sparks Twitter: https://twitter.com/SparksMaths More of Ben on Numberphile: https://youtu.be/ETrYE4MdoLQ https://youtu.be/kbKtFN71Lfs Geobra file relevant to this video: https://www.geogebra.org/m/uPTEQnZs Infinity with James Grime: https://youtu.be/elvOZm0d4H0 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9
  • Tree Gaps and Orchard Problems - Numberphile etiketleri


  • There is a German saying: "Den Wald for lauter Bäumen nicht sehen" / "To not see the forest because of too many trees" .. This suddenly makes sense.

  • I love the "mindfuck" aspect of mathematics and I always have. It's stuff like this where reality and intuition are on complete opposite ends of the spectrum that I love the most.

  • Pi, fibonacci, golden ratio, probability, magnitudes of infinity, Riemann zeta function... it's like all these years of watching numberphile has prepared us for this one video lol

  • So if I'm understanding this correctly you would see no trees since in-order to see something that is a point (infinitely thin trunk) you would need to have them in every direction you look so every point is blocked out and you see a "solid" wall but since there are infinitely more gaps due to irrational fractions than there are blocked points you see no trees. That is wild isn't it!?

  • So many shout outs to Dr. James Grime. It's like he knows he's the best Numberphiler.

  • This infinite orchard almost solved world hunger, but unfortunately the harvesters couldn't find any trees since they were all points and had a 0% chance of being seen.

  • What does it mean that the golden ratio is "the least well approximated by a rational number"? I'd like to see a video just about that. It sounds like a very interesting property.

  • Somewhat unrelated but I was told by a guy who works in forestry that sometimes trees are planted in a fibonacci arrangement to maximise sunlight exposure. In a spiral like that seen in the centre of a sunflower

  • This was brilliantly presented and really fun. I would never think of this type of problem but I am super glad to have stumbled upon the fact that this kind of thinking exists!

  • The golden ratio strikes again.

  • If a mathematician walks into an orchard

  • If a tree falls in an infinite forest but you're looking in an irrational direction, does it make any sense?

  • That was pretty cool actually. Weird maths turning up in places you don't expect is always great fun

  • The Fibonacci bit at the end there really blew me away.

  • You would see -1/12th trees.

  • Seems like a Parker forrest to me. It's there, but not really.

  • Clickbait title: "Mathematician proves that you can't see forest for the trees"

  • I'm going to look along a gradient of TREE(3)

  • Every direction you look you won't see a tree sounds like something out of the Hitchhiker's guide.

  • If an infinitly thin tree falls in the forest and you're standing at the edge, does it make a sound, and do you see it?