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?Full answer (spoilers)
The path traced out by the tip of the shadow can be...
1) A circle (if you are on one of the poles during their summer)
2) An ellipse (if you are in the Arctic or Antarctic circle, but not on either pole, during a day where the sun doesn't set)
3) A line (this happens if you are anywhere on Earth besides the poles, during either the Spring or Autumn equinox)
4) A parabola (this happens if you are in/on the Arctic or Antarctic circle during a day where the sun BARELY sets, meaning it sets and rises in the exact same location. This happens twice a year for any point in those circles. If you are ON one of the circles, then it will happen during the Summer or Winter solstice for the Arctic and Antarctic circles respectively).
5) A hyperbola (If you aren't in one of the places listed above on those specific days, then you'll get this shape. This is what happens at most places on Earth throughout most of the year).
?Resources
Interactive tool: https://www.geogebra.org/m/AHEgBVUd
Video showing linear path on Equinox: https://www.youtube.com/watch?v=Wz-nXJYUDhI&t=1s
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The reflector in the flashlight has the bulb in the Loci of a PARABLOIC Dish to have the light leave straight out. It is So a candle is a better demonstration tool.
@Orion6479 Says:
It is so hard to take you seriously after all those sketches 😂
@대한민국만세-p6p Says:
Goood!! 😍😍😍
@paulmanhart4481 Says:
Very interesting. Thanks.
Check out a paper I wrote called “Swept Conics”. I think it was at the 2010 International Optical Design Conference. But maybe the 2006.
Hammer a nail at one of the focal points of a conic and sweep it about that axis. Lots of fun stuff. I got a patent on some of this stuff for applications to optical systems, like converting a point source to a diffraction limited line or arc of light. I was surprised to see that Bang and Olufsen has a speaker (Beo 5) that uses this exact concept for an acoustic lens. They place a speaker at the focal point of a tilted ellipse and it spreads the sound out into a 180 degree arc.
Conics are fun.
Thanks for the tutorial here.
@J1Bracket-lf9pn Says:
Woah! I just now realized that "conic sections" is referring to sectioning (i.e., slicing through) cones. When I was in high school and my teacher said we were going to begin studying conic sections, I thought she was referring to the sections of the textbook dealing with conics. That was 25 years ago. I've since earned a EE degree and have been immersed in mathematics for most of my life at this point. Yet, I'm just now putting it together after seeing your video thumbnail. I feel both dumb and enlightened. Well done!
@IshrakIfti Says:
I really wanted to see how conic sections change with eccentricity, but couldn't find anything that was satisfying and intuitive. Like at which point does a parabola becomes an ellipse? All of a sudden, found this video. Thank you so much for this! This is exactly what i wanted to see!
@chandanapalit5674 Says:
You need a Nobel 🎉🎉
@huddy2463 Says:
for some reason i feel like i know zach personally just from the way he talks
@matheo6462 Says:
I thought you were Patrick bateman, and so I stay........
@Michael-vf2mw Says:
Zach deserves a prize for how smoothly he was able to throw a burn into the first 20 seconds.
@benberlowitz6381 Says:
This is all wrong because the earth is flat.
@henryrahoni8772 Says:
I never knew this channel existed lmao. Go Jesus!
@BaconJD420 Says:
Quit ballsplaining, not one intelligible concept herein
@chewymustard Says:
Me in southern alabama wondering why the sun is above me at noon sometimes 💀💀
@alejrandom6592 Says:
1:31 I felt so smart and so stupid at the same time
@gesellschaftskritischer_7360 Says:
Flat earthers gonna love this video
@JoshuaGutz Says:
What about the lesser known conic section of two intersecting lines? From the equation x^2=y^2, with two intersecting line solutions of y=x and y=-x.
@TrimutiusToo Says:
Inside the arctic circle you can have an elliptical sundial... At least one actually exists from what i know
@alangrant5278 Says:
Hmm there ain’t no South Star for the Southern Hemisphere but you can work out south from the Southern Cross
@memerightsactivist7972 Says:
Always nice to see he’s still hilarious on the main, educational channel
@AskAKill99 Says:
Funny when he said if you've never seen a cone cut in half in real life "then you're wrong"
@ramonlantigua2030 Says:
I 😘 be the video but this can be used as flat earth propaganda so be careful how you word things in it.
@TepsiMorphic Says:
I had to write a 5 pages paper for a project in my analytical mechanics class. The topic was the two-body problem under the Kepler potential (that is a potential that's prop. to the invers of the distance). One part of the project is to investigate what types of orbits that can be obtained given the initial conditions and the system (the two bodies) and it turned out to be conic sections. It's just so wonderful how we are surrounded by patterns.
@JustRollin Says:
Zach is the type of guy who makes a video about conic sections.
@28aminoacids Says:
Wait, isn't the axis of rotation of earth in 66° angle with the plane of it's revolution around the sun?
@Global-yt Says:
5:13 "This is the idea for most people" My brother half the world lives in East/South Asia
It's just the Western world (which to be fair has the most YouTube viewers in general) that revolves on that axis
@BlastinRope Says:
Shut up nerd
@teucer915 Says:
"Here we got the earth, chilling" made me immediately want to fire ze missiles
@sankalppatidar4975 Says:
2:10
@pedrocapitao9268 Says:
1:30 Very cool
@smallguy1113 Says:
5:05 bro excluded everyone in china and India, some how they don't count as "most people"
@maybeinactive Says:
This video ended up teaching me more about earths rotation than the conic sections
@anonymous_TAS Says:
Wow, that was fantastic. Thanks!
@Jaylooker Says:
Nice
@Qermaq Says:
Technically, the relationship between the Earth and the Sun changes slightly through the day. So the shape will probably be a slightly warped hyperbola, starting out as one and finishing as another that's a tiny bit different.
@taktoa1 Says:
You forgot to include the case where you are in the arctic/antarctic circle during winter, in which case the set of shadowed points over the course of a day is empty.
@anizulrehman2231 Says:
HEY ZACH Plzz answer my question I will be grateful to you.ANY BOOK RECOMMENDATIONS.
It helped me a lot. I am a 10th grad student . Below is question.
Please read every line before answering my question and try to answer as best as you can.
I don't want to study math without true understanding.Conceptual knowledge is not understanding. All the Books that I have read till date describe things in an abstract manner without any context. And even worse, they always make assumptions that turns the material inaccessible.For a long time, the way I have done math in general is to sometimes just accept things as they are. For example, Pythagoras Theorem states the way to find the hypotenuse of a right angle triangle. How (the proof or 'why' it works)? Doesn't matter, just do it and you find the answer. Why forumula works.This has scaled up to my current position .
While I enjoy math, and am very good at it from conventional standards (getting A/A* predicted on tests, and breezing through the books), I constantly feel that I dont really know where it comes from. Yes, the basics are there (a circles chord when bisected passes through the centre, proof by standard pattern spots in integration, etc) but I always find myself asking WHY thats true. I get the answer in the end but I dont really know what I am doing. This problem really shows itself when I deal with abstract questions (or 'fun' questions) you find in olympiads and the like. The solutions seem so simple and I cant help but appreciate them but for whatever reason I can rarely do them. The way I tried to overcome this is by covering topics I had just accepted to always work and understand their core concepts.
And this relates to my question. I cant stop myself from asking WHY that work.
Any book recommendations
@natenoisy7571 Says:
wow, this was pretty cool to know. the visuals were really helpful
@nalat1suket4nk0 Says:
cool
@shisir_nayak2377 Says:
The relatibility between sun shadow and conic sections is unexpected. You made me a little less dumb.
@nick-paris Says:
Imagine how mind blown people were when the discoverers of these mathematics shared them with people of their time. I am equally mind blown. This is by far the best explanation of the sun's position in the sky over the year I have ever seen. My highest praises to you Zach
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