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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 LessonThere 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 PottsI 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.

HasekuraIsunaPi, 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

Cody'sLabSo 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!?

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

Seth PersonThis 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.

eggoryWhat 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.

TibeesSomewhat 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

fprintfThis 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!

myantispamboxThe golden ratio strikes again.

Chris StarIf a mathematician walks into an orchard

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

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

thatdearguyThe Fibonacci bit at the end there really blew me away.

NilguiriYou would see -1/12th trees.

Martin KSeems like a Parker forrest to me. It's there, but not really.

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

AlanKey86I'm going to look along a gradient of TREE(3)

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

Goran NewsumIf 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?