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The Surprising Uses of Conic Sections
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- Опубликовано: 18 авг 2024
- Conic sections - the curves made by slicing through cones at various angles - were studied by the ancient Greeks, but because of their useful properties, have many real-world uses. Planets have elliptical orbits, projectiles move in parabolas, and cooling towers have hyperbolic cross-sections. But did you know that one of the most important curves in economics is a hyperbola? Or that ellipses are used to cure kidney stones?
A lecture by Sarah Hart
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If we ever get lost in the desert with only a string and 3 sticks or branches as tools, and need to draw an elipse - now we know how to do it.
The Surprising Uses of Conic Sections 1903pm 27.4.22 ok; i am of an age wherein can recall using pound notes as legal tender... eg: 1 quid 25p for 5 days worth of school dinners... though that has nought to do with newton or elliptical orbs. my were glazed over for quite some time...
Could be a life saver!
@@fburton8 You never know when you need an elipse!
Cane here from the cycloid video, great stuff!
*Sarah:* _blah blah blah_ Hyperbola _blah blah blah_
*Me* (channeling my inner Key & Peele): I wish I was high on Perbola.
I'll take my comedy medal of honor now, thank you!
Now I've learnt how to shape a nice eliptic garden/lawn. But I don't know how to calculate the length of fence I need to go around it. But if I tie my two dogs - one at each end of a long leash, and let it run through a loop, attached to the ground...
The Surprising Uses of Conic Sections 1845pm 27.4.22 i forgot.. what's the conic principle???? i did read up on it once... but i have forgotten. leaving me to assume that it mustn't have been important...
How to calculate the length of fence? Don't. Measure it. That is not a calculation that you ever wish to carry out. There is no computable equation for the perimeter of an ellipse - at best there is an infinite series that converges upon it, which can be used to give you an answer to a sufficient level of precision for practical purposes.
Plus you only need one dog for your elipse-drawing - you peg the string at both ends, and run it through a loop on the dog's harness.
@@vylbird8014 I must have been tired last night. Now, trying to think of the two dog scenario it's just a mess. :D But one dog as you explain could work, and then you don't need the fence for the dog. ("Tired" to make stupidity seem more temporary. ;) )
Thx. Great lecture. Geometry is a foundational principle of our universe. Geometry intersects with a lot of descriptive math. Personally I think space-time Geometry produces math. I investigate geodesics, geometric termination and singularities.
How did this happen... I was just talking about conical shapes somewhere else. This happened within minutes of each other.
Destiny?
Serendipity
It's divine providence. There are no coincidences.
Another use is in *Elliptic-Curve Cryptography.* But that's an obvious one and everybody knows it, so she didn't mention it.
It seems counter-intuitive that an ellipse is formed by slicing through a cone at an angle. The upper slice passes through a smaller diameter of the cone than the lower. To me, this would suggest the shape formed could not be symmetrical.
i was thinking the same, you should have an egg or teardrop.
there must be something in the definition of a conic that includes cylinders. they are probably defined due to the angle of at their cross section on axis of symmetry. Cylinder is 0 degree/ parallel case?
@@mistermoggy8707 The angled cross-section of a cylinder is also an ellipse, but the key difference with the conic construction is in how the focii are defined.
If you imagine in both cases starting with a horizontal circular cross section and tilting it slightly to form the elliptical cross section. For a cylinder one focus will move above and one below the initial circle to give two focii equidistant from the original centre.
For the conic, the centre of the original circle will remain as one focus and the other focus will always move downwards vertically as you increase the angle/ eccentricity. Increasing the angle here is equivalent to increasing the radius of the great circle as in the rainbow diagram.
This probably doesn't do much to prove that it'll always be an ellipse but might help visualise what's going on. Remember as well that horizontal diameter doesn't mean much when you're doing an angled cross section.
It could have been interesting, but the sound quality is poor.