Spherical Geometry in Navigation
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- เผยแพร่เมื่อ 5 ก.พ. 2025
- Spherical geometry is any geometry occurring on the 2-dimensional surface of a sphere. Even though the axioms for spherical geometry are similar to those of Euclidean geometry, there are some fundamental differences that create unique situations such as triangles with interior angles totaling greater than 180 degrees. Due to the Earth’s spherical nature, spherical geometry is incredibly important in navigational techniques since the shortest distance is no longer what we might consider a “straight” line. In this presentation, we explain the fundamentals of spherical geometry and how it is used in navigation, specifically in modern day air travel.
Made by: Arvind Arikatla and Rebecca Glowinski
![Non-Euclidean Geometry [Topics in the History of Mathematics]](/img/n.gif)
Oh my God thank you... This basically destroys flat earthers
Several observations destroy the flat earth.
This is what I was looking for to understand spherical geometry triangle. Well explained! Thank you very much!
It's like boxing with my brain. I'm not sure who's winning, but I am learning. Thank you!
Thank you! It’s helping me figure out the model for Sepharial’s teaching
you really can explain this topic. Great job!
It becomes clearer when you project this on Google Earth.
I did the exact same thing
Google maps, regardless of its visual representation, is a flat plane with no positive curve whatsoever. NASA's Spherical system is completely untenable from a navigational perspective, being as we don't live on a planet.
@@homelesshendrix Who ya kidding?
You can't navigate and don't know the first thing about it.
You're embarrassing yourself.
It was interesting video! But what it's missing is an illustration on how straight line what look on a sphere and why it's actually longer.
Thanks for your nice explanation.
Still, I am doubtful about the example on flight path between Manila, Philippines and Florida, USA.
good it shows you have a functioning brain. One could EASILY place a plane and its attendant circle between W Palm ( Boca has no International airport)and Manila or any other place
@@yupok318Good, now explain a direct flight between Sydney and Johannesburg. Not a single flatearther has been able to give a valid explanation.
What would be the best device to measure this in the real world? And fwiw, this is spherical trigonometry not "spherical geometry" as there are no Euclidean straight lines in "spherical geometry."
Spherical geometry is a non Euclidean geometry.
@@eMBO_Gaming spherical trigonometry is Euclidean and this is 100% spherical trigonometry as all of the functions require straight lines.
I still dont understand...
The curve is already counted in on a flat projection of the earth.. thats why continents and states are distorted. So wouldnt that mean that the shortest path on a flat projection of the earth would be a straight line...
yes and irl it would be curved
My understanding that has been that Euclid was doing his geometry on a 2-d plane and that it wasn't until Gauss measured the region around Gottengen in a large survey map, that it was that the differences were discovered between the two.
Didn’t know that….
Its my understanding Euclid was the Last real Mathematician, and everyone after him violated his 5th postulate, thus creating an imaginary world where parallel lines intersect, and we are now living in a non-Euclidean matrix that is a complete hoax.
The Shortest distance between two points on the surface of a sphere are Two Geodesic Arcs equidistant in lenght and a Mirror image of each other unless the points are 180 degrees apart Antipodes (POLES). Then its one line around the meridan only .(The only real great circle route )....This does not happen in Reality esp with flight routes ......Its Flat
nice
@Easton Klayh AAAAAAAAAHHHHHHHHHHHHH EEEEEEEEEEEEEEEEEEE
Are you able to provide a practical example of this?
For example, with a theodolite.
did sailors use this in ancient times too
They were more genius than us...
Yes.
@@lipikabhar1700 ‘way more genius than us’ ~ actually, not true, but you are making a strong argument…
@@lipikabhar1700 in Hygiene no but in maths yes
Sailors have always used plane geometry, excepting the ones who got lost. the Sea is 'level and longitude lines grow further apart the further south the latitude. Great Circle sailing is a completely bogus application. Earth is not a planet, much less a globe.
Me who understands
But can not answer
4:32 that is not true the shortest distance between two two points on a sphere horizontaly layed on the same small cirrcle is that small circle.
5:43- no. Antipodal means opposite feet. And it is as ridiculous as it sounds, just ask Alice.
The term he used was antipodal points.
'In mathematics, antipodal points of a sphere are those diametrically opposite to each other (the specific qualities of such a definition are that a line drawn from the one to the other passes through the center of the sphere so forms a true diameter).[1]
This term applies to opposite points on a circle or any n-sphere.'
Thanks the earth is flat and round !!
Since the earth is not a sphere, spherical geometry is begging the question.
thats why elliptical trigonometry accounts for that discrepancy.
What are you doing here, Travis?
Shouldn't you be trying to determine the diameter of your stupid flat earth? Or describe a coordinate system.
All flight planning software uses an ellipsoid (like WGS 84) and a hundred thousand flights per day arrive at their destination. So I'd say that the predictions of spherical/ellipsoidal geometry as it relates to the Earth have been verified literally millions of times.
Cool, so not only do you come here to announce how dumb you are you are kind enough to give a twofer in only one sentence.
Well done.
If you are actually suggesting planes navigate using spherical geometry and the Great Circle, that flies in the face of reality. Planes use the polar coordinate system, which is cartesian in nature, just with zero at the center point directly under Polaris. Earth is not a planet, to begin with, and certainly all patents for aircraft are based on a fixed plane, i.e. flat earth. So you are lying to yourself and living a total fantasy if you think aircraft follow a curved path of any sort. The path is curved because the maps are curved. Look at the flight path on an Azimuthal Equidistant map and you will see its a strait line over a level plane.
I hope you realise that the polar coordinate system is 3D and uses spherical coordinates.
@@haven216 How so? polar coordinates have the north pole at the center of an x,y,z axis with everything in the positive y quadrants above sea level. Spherical and cartesian coordinates are the same things in this sense.
Mindless flattard garbage.
The distance from Johannesburg to Sydney is 12000km. Direct flights between the two cities are conducted weekly.
On a moronic flat earth the straight line distance is more than 23000km. There is no commercial aircraft capable of revenue flight across that distance.
You flattards suck at basic geometry.
@@TruckerCarlson- congratulations, you are 100% incorrect.
In a three dimensional Polar coordinate system, points are defined by a distance from the origin and two angles from two reference planes (usually orthogonal)
which is completely different from a Cartesian coordinate system where points are defined by three distances from the origin along three (usually orthogonal) reference planes.
“Planes use the polar coordinate system, which is Cartesian in nature”...
This is hilarious to anyone who has studied anything more than the most basic geometry.
Wrong
That is a lot of imagining
Um it's either a line or it ain't. Calling circles lines is just BS.
To me this proves that the earth is flat after all and I dont need mental gymnastics to try to show otherwise.
Reality is independent on what you are able to grasp or not.
@@AlexFoxthrot Good one!
You are not qualified to have this conversation.
Lines can be curved in math...
they literally are in spherical geometry though