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# 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

Daily Drum Lesson1 year agoThere 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.

Kevin Potts1 year agoI 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.

HasekuraIsuna1 year agoPi, 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

Tibees1 year agoSomewhat 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

Cody'sLab9 months agoSo 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!?

Seth Person1 year agoThis 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.

Sebastián Espejo Loyaga1 year agoSo many shout outs to Dr. James Grime. It's like he knows he's the best Numberphiler.

eggory1 year agoWhat 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.

myantispambox1 year agoThe golden ratio strikes again.

fprintf1 year agoThis 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!

Adam Weishaupt1 year agoIf a tree falls in an infinite forest but you're looking in an irrational direction, does it make any sense?

Chris Star1 year agoIf a mathematician walks into an orchard

Tricky1 year agoThe Fibonacci bit at the end there really blew me away.

The Gentle One1 year ago (edited)Cast: Riemann's Zetafunction, the Golden Ratio, the Fibonacci Sequence, Pi, Primes

Dave Curran1 year agoHere is Douglas Adams using the same maths: “It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.”

ardenthebibliophile1 year agoI think if you’re allergic to apple trees and find yourself in the middle of an infinite apple forest you’ve made some wrong choices in life!

Manuel Brand1 year agoMoral of the story:

Martin Heermance1 year agoEvery direction you look you won't see a tree sounds like something out of the Hitchhiker's guide.

Tymoteusz Czech1 year agoClickbait title: "Mathematician proves that you can't see forest for the trees"

MishapTrap1 year ago"There is unrest in the forest, there is trouble with the trees, for the maples want more sunlight, and the oaks ignore their pleas."