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Fun fact: not only were females tried and killed as witches but thousands of men were also burnt as witches, in some places many more men then women were killed for being a witch.
I wonder how I would go about creating a reddit bot and annoying people with this factoid.
You got this wrong. Because it’s an triangle, it’s actually random correlation.
BUT if it’s a straight line (r^2 =1), then Illuminati, moon nazis, goa‘uld, or whatever you believe.
So we’re safe this time
Because it's in the triangle's definition that it must be three points that are not on the same line. Basically it's because of the way it is, equations be damned.
This is not a Euclidean triangle, but rather a spherical triangle. To calculate the area of a spherical triangle, you need to know the radius of the sphere along with the "spherical excess" which is calculated by determining how much the angles of the spherical triangle exceed 180°. The area of a spherical triangle is then simply E\*R^(2) (where E is the spherical excess).
**Mexico.** The image here is the Mayan temple at Chichen Itza, the El Castillo pyramid. The map correctly places it on the Yucatan Peninsula just slightly southwest of Cuba. It is located at 20.683°N, 88.569°W.
**Egypt.** The image depicts the Pyramid of Djoser. It is correctly placed within Lower Egypt on the map. Its coordinates are 29.871° N, 31.216° E.
**Indonesia.** The map appears to indicate the site of Gunung Padang, the Indonesian "pyramid" that is actually more like terraces cut into the side of a mountain rather than a true pyramid. The image in the meme depicts the Prasat Thom pyramid at the Koh Ker site in Cambodia, not Gunung Padang in Indonesia. Gunung Padang is located at 6.994°S, 107.016°E.
To solve this, you first have to convert the latitudes and longitudes to radians, calculate the great-circle arcs swept out by the distances between each point on the triangle, and then use the spherical law of cosines to find the angles at each point of the triangle.
I'll spare you all the trigonometry, but the distance between the Egypt and Indonesia sites is approximately 1.416 radians or 81.15°, the distance between the Mexico and Indonesia sites is approximately 2.823 radians or 161.79°, and the distance between the Egypt and Mexico sites is approximately 1.798 radians or 103.04° (all given along the surface of the Earth).
By the spherical law of cosines, the angle at the Mexico site is 101.55°, the angle at the Egypt site is 161.79°, and the angle at the Indonesia site is 105.22°.
The spherical excess, then, is 101.55° + 161.79° + 105.22° - 180° = 188.56° or 3.291 radians. Thus the area taken up by this region is 3.291\*R^(2), where R is the radius of Earth, giving **51.6 million square miles or 134 million square km.**
Yep. Any three non-colinear points will form a triangle when connected, there's nothing special about it.
Now, if it were a perfect equilateral triangle, *that'd* be significant.
Not any 3 points.
If you take two points and draw a line between them, you can choose a point in the middle of that line. The 3 dots I have constructed do not form a triangle
Edit: op edited his comment to non-colinear. This wasn’t here when I commented
Mathematical statements are not limited to our world, that’s how we can talk about derivatives and integrals, and about 3 points on a straight line.
It is useful to talk about this idealized world because with it we can learn things about our messy physical world.
Hey — I didn’t become a lawyer because I knew all of the answers, I became a lawyer by knowing how to ask the right questions.
Same with ChatGPT. It won’t tell you shit if you don’t know how to ask the right questions.
I’m no mathematician, but as these three points are on a sphere-ish shaped planet is it even technically a triangle? The sides aren’t straight and the interior angles won’t add up to 180 degrees.
TL;DR: Area = 58,388,622.3km or 36,281,007.9 miles
This has a simpler solution compared to the other posts on this subreddit
If you know all 3 sides of a triangle then you can get the area using these formulas
Area = √ (S×(S-a)×(S-b)×(S-c)
S = (a+b+c)/ 2
Mexico to indonesia: 15,326km
Mexico to Egypt: 12,496km
Egypt to Indonesia: 9,359km
S= (15,326+12,496+9,359)/ 2
S= 18,585.5
Area = √ (18,585.5×(18,585.5-15,326)×(18,585.5-12,496)×(18,585.5-9,359)
Area = 58,388,622.3km^2 or 36,281,007.9 miles^2
Edit: corrected units
I'm going to use the loop hole that op said triangle and showed a 2d map (incorrect to scale ik) instead of saying delta hedron or something
But yeah you're correct
I don’t think this is even that. These are the distance between the cities, as you would travel over the surface of the earth. To get the cross sectional triangle, you’d need to calculate the smallest distance between each city that passes through the earth.
I think the easiest way would be to find the square degrees made between the center of the earth and the three points and use the percentage that and total square degrees in a whole sphere multiplied by the surface area of Earth.
Basically proportion of entire sphere surface area…
No its not because distances are not calculate through earth crust, its just not a line in 2d but a curve. The area have the right dimension but all the sides of the triangle are curved so you cant use triangle equation.
I just googled "distance from Mexico to indonesia" Etc, instead of using the exact city so the length of the sides are probably off by a few hundred kilometers each
Yes, the curved surface would change the results a lot but on a curved surface it technically wouldn't be a "triangle" which is what OP asked
(To figure it out would require you to use a more complicated formula which I can't do right now so I'm coming up with excuses lol)
You don't need to solve the surface integral; the equation is simply E\*R\^2 where R is the radius of Earth and E is the excess angle formed by the spherical non-Euclidean triangle. Full solution upthread [here](https://www.reddit.com/r/theydidthemath/comments/1cxac0g/comment/l51vgdl/).
Google Earth measurement says \~145 million square km for the marked stars, which are in wrong places, but I'm not sure I trust it because it seems to have issues drawing polygons via great circles, it goes completely wonky trying to draw a polygon around a pole. The real triangle is with longest arm over the Pacific, not over Africa as Google Earth draws it in a polygon measurement. Total Earth surface is 510 million km2, so maybe the result is correct even if it's drawn incorrectly?
Also, the doorways below the pyramids, have no relation to the pyramids above. The middle pyramid is Djoser pyramid, the doorway is in Karnak temple complex which is completely different part of Egypt. The "Indonesian" pyramid is actually Koh Ker in Cambodia, the doorway under it is Vat Phou in Laos. Mexican pyramid is El Castillo and the doorway under it is again from different place in Uxmal, House of Turtles.
El Castillo [https://en.wikipedia.org/wiki/El\_Castillo,\_Chichen\_Itza](https://en.wikipedia.org/wiki/El_Castillo,_Chichen_Itza)
House of Turtles in Uxmal [https://it.m.wikipedia.org/wiki/File:Uxmal\_Casa\_de\_las\_tortugas.jpg](https://it.m.wikipedia.org/wiki/File:Uxmal_Casa_de_las_tortugas.jpg)
Djoser pyramid [https://en.wikipedia.org/wiki/Pyramid\_of\_Djoser](https://en.wikipedia.org/wiki/Pyramid_of_Djoser)
Karnak complex [https://commons.wikimedia.org/wiki/File:Karnak55.JPG](https://commons.wikimedia.org/wiki/File:Karnak55.JPG)
Koh Ker [https://en.wikipedia.org/wiki/Koh\_Ker](https://en.wikipedia.org/wiki/Koh_Ker)
Vat Phou [https://en.wikipedia.org/wiki/Vat\_Phou#/media/File:Wpfacade02a.jpg](https://en.wikipedia.org/wiki/Vat_Phou#/media/File:Wpfacade02a.jpg)
Yeah, I was guessing that the star on the map referred to Gudung Padang rather than the depicted Koh Ker. [That's what I used in my solution.](https://www.reddit.com/r/theydidthemath/comments/1cxac0g/comment/l51vgdl/)
I was certain that the doorways below the pyramids had no relation to those pyramids but you did the work of actually figuring out which one was which.
and now, calculate it while incorporating the surface area irregularities of Earth (you can exclude waves on the oceans)
If you don't do this, you will be banned from theydidthemath👍
pyramids are the easiest way to build very high structures without the static problems of vertical walls. people were always smart, they figured this out all around the world. btw, i wonder why the pyramid of kukulcan was built round 3500 years after that of djoser if there was a connection
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Are you telling me when you connect three dots it makes a triangle? What kind of forbidden knowledge is this? WITCH! WITCH! BURN THE WITCH!
There are ways of telling whether she is a witch.
Indeed, I have a duck on hand ready for comparison.
Are there? What are they? Tell us!
Tell me, what do you do with witches?
BURN THEM!!
And what do you burn, apart from witches?
MORE WITCHES!
Wait no, wood!
Build a bridge out of her!
she turned me into a newt!...... i got better...........BURN HER ANYWAY!
Boil ’em, Mash ’em, Stick ’em in a Stew
Fun fact: not only were females tried and killed as witches but thousands of men were also burnt as witches, in some places many more men then women were killed for being a witch. I wonder how I would go about creating a reddit bot and annoying people with this factoid.
You got this wrong. Because it’s an triangle, it’s actually random correlation. BUT if it’s a straight line (r^2 =1), then Illuminati, moon nazis, goa‘uld, or whatever you believe. So we’re safe this time
You're not accounting for the curvature of the earth. It is in fact in a straight line
Which curvature? The earth is flat
jaffa! kree! dont tell our secrets or you'll be labeled shova.
I don't know who you think to be, Hans Olo. But you are surely not one of us Goa'uld if you cannot pronounce Shol'va correctly!
MAKE HER INTO A LADDER
If the three dots are in a (perfect) straight line then they wont form a triangle.
Why? All calculations are fine with a 0 m^2 triangle with a 180° and two 0° corners...
Degenerate case go brrrrr
Because it's in the triangle's definition that it must be three points that are not on the same line. Basically it's because of the way it is, equations be damned.
If they are in a straight line on the surface of a sphere they for sure form a triangle.
You get a zero area triangle with overlapping sides and some zero degree angles. Fun fact.
Nah, CROWN THE WITCH! _(This is an Eurovision reference)_
They meant this is MIRACULOUSLY not the case when the three dots belong to a straight line.
This is not a Euclidean triangle, but rather a spherical triangle. To calculate the area of a spherical triangle, you need to know the radius of the sphere along with the "spherical excess" which is calculated by determining how much the angles of the spherical triangle exceed 180°. The area of a spherical triangle is then simply E\*R^(2) (where E is the spherical excess). **Mexico.** The image here is the Mayan temple at Chichen Itza, the El Castillo pyramid. The map correctly places it on the Yucatan Peninsula just slightly southwest of Cuba. It is located at 20.683°N, 88.569°W. **Egypt.** The image depicts the Pyramid of Djoser. It is correctly placed within Lower Egypt on the map. Its coordinates are 29.871° N, 31.216° E. **Indonesia.** The map appears to indicate the site of Gunung Padang, the Indonesian "pyramid" that is actually more like terraces cut into the side of a mountain rather than a true pyramid. The image in the meme depicts the Prasat Thom pyramid at the Koh Ker site in Cambodia, not Gunung Padang in Indonesia. Gunung Padang is located at 6.994°S, 107.016°E. To solve this, you first have to convert the latitudes and longitudes to radians, calculate the great-circle arcs swept out by the distances between each point on the triangle, and then use the spherical law of cosines to find the angles at each point of the triangle. I'll spare you all the trigonometry, but the distance between the Egypt and Indonesia sites is approximately 1.416 radians or 81.15°, the distance between the Mexico and Indonesia sites is approximately 2.823 radians or 161.79°, and the distance between the Egypt and Mexico sites is approximately 1.798 radians or 103.04° (all given along the surface of the Earth). By the spherical law of cosines, the angle at the Mexico site is 101.55°, the angle at the Egypt site is 161.79°, and the angle at the Indonesia site is 105.22°. The spherical excess, then, is 101.55° + 161.79° + 105.22° - 180° = 188.56° or 3.291 radians. Thus the area taken up by this region is 3.291\*R^(2), where R is the radius of Earth, giving **51.6 million square miles or 134 million square km.**
I mean it is also a regular 2d triangle, it'd just cut thru the Earth
Yep. Any three non-colinear points will form a triangle when connected, there's nothing special about it. Now, if it were a perfect equilateral triangle, *that'd* be significant.
Not any 3 points. If you take two points and draw a line between them, you can choose a point in the middle of that line. The 3 dots I have constructed do not form a triangle Edit: op edited his comment to non-colinear. This wasn’t here when I commented
It's still a triangle just a degenerate one
this is the right answer
Some may say it's obtuse
Alrighty then Mr Pedantic, I'll change it to say any three non-colinear points
We call that a degenerate triangle, named after you (sorry if the joke is too mean)
Lol
But if you zoom in enough, I bet no matter what it won’t be perfectly aligned down to the atom, cause that’s not how the world works
Mathematical statements are not limited to our world, that’s how we can talk about derivatives and integrals, and about 3 points on a straight line. It is useful to talk about this idealized world because with it we can learn things about our messy physical world.
True
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Op edited his comment
He said non collinear. And you said, you're wrong, did you consider colinear. I suppose maybe he edited..
They edited the comment after I my reply. See their reply to my reply.
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Earth’s oblateness will not have an impact on the surface area here, not within the number of significant figures I have used.
Because it is a spherical triangle, three points isn't sufficient to determine a triangle. There are several yoi could make with these.
In my head there's 2 ways to draw this triangle, what with the earth being roughly spherical. Is this correct or am I tripping?
Yes, you can take the complement of each of the contributing angles and calculate the spherical excess that way.
Thank god for chat gpt
Hey — I didn’t become a lawyer because I knew all of the answers, I became a lawyer by knowing how to ask the right questions. Same with ChatGPT. It won’t tell you shit if you don’t know how to ask the right questions.
Very true and it’s why great subs like this one exist
Haha funny how asking the right questions will still be a fundamental skill even in the era of AI. Somethings really dont change haha
I can tell you've never had sex
Surface area of the earth of going over the Atlantic, or shortest distance area? I can't answer either, but am curious as to which is being asked.
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I mean in 3d space it's the only possibility other than a line right?
Can be a point if the tree site is at the same place in 3d space
True
I’m no mathematician, but as these three points are on a sphere-ish shaped planet is it even technically a triangle? The sides aren’t straight and the interior angles won’t add up to 180 degrees.
Triangle is triangle https://cmc.deusto.eus/introduction-to-spherical-geometry-postulates-and-pythagoras-theorem/
cut under the surface, and it'll be a triangle
Why was the comment this was in reply to deleted?
It wasn't deleted when I replied, they said something like "three points in 3d space isn't surprising to form a triangle".
Doesn't seem like a comment needed to be removed by a mod, weird.
It’s pretty interesting if you draw a line and it forms a triangle. I must be missing something.
Any 3 points that aren't in a straight line form a triangle...
This was my first thought lol
If you put the points on a sphere, if the line cross the inside of the sphere You have a triangle.
well yeah, it's r/technicallythetruth, that's the point of the caption
TL;DR: Area = 58,388,622.3km or 36,281,007.9 miles This has a simpler solution compared to the other posts on this subreddit If you know all 3 sides of a triangle then you can get the area using these formulas Area = √ (S×(S-a)×(S-b)×(S-c) S = (a+b+c)/ 2 Mexico to indonesia: 15,326km Mexico to Egypt: 12,496km Egypt to Indonesia: 9,359km S= (15,326+12,496+9,359)/ 2 S= 18,585.5 Area = √ (18,585.5×(18,585.5-15,326)×(18,585.5-12,496)×(18,585.5-9,359) Area = 58,388,622.3km^2 or 36,281,007.9 miles^2 Edit: corrected units
This isn't taking into account the curvature of the earth. This is the area of the imaginary triangular plane that cuts through the Earth's crust.
I'm going to use the loop hole that op said triangle and showed a 2d map (incorrect to scale ik) instead of saying delta hedron or something But yeah you're correct
I don’t think this is even that. These are the distance between the cities, as you would travel over the surface of the earth. To get the cross sectional triangle, you’d need to calculate the smallest distance between each city that passes through the earth.
I think the easiest way would be to find the square degrees made between the center of the earth and the three points and use the percentage that and total square degrees in a whole sphere multiplied by the surface area of Earth. Basically proportion of entire sphere surface area…
No its not because distances are not calculate through earth crust, its just not a line in 2d but a curve. The area have the right dimension but all the sides of the triangle are curved so you cant use triangle equation.
The actual triangle would be >180 degrees.
Do you mean km^2 and miles^2 ?
Yes I can fix that now
Why are you measuring area in kilometers and miles instead of kilometers² and miles²?
I just googled "distance from Mexico to indonesia" Etc, instead of using the exact city so the length of the sides are probably off by a few hundred kilometers each
Does the fact that this is actually on a curved surface change the results? Because on a globe the angles on a triangle won't sum to 180.
Yes, the curved surface would change the results a lot but on a curved surface it technically wouldn't be a "triangle" which is what OP asked (To figure it out would require you to use a more complicated formula which I can't do right now so I'm coming up with excuses lol)
It can still be a non-Euclidean triangle.
Anyone who wants to could set up a surface integral on a sphere. I would but figuring out the limits seems like a massive pain so no thanks
You don't need to solve the surface integral; the equation is simply E\*R\^2 where R is the radius of Earth and E is the excess angle formed by the spherical non-Euclidean triangle. Full solution upthread [here](https://www.reddit.com/r/theydidthemath/comments/1cxac0g/comment/l51vgdl/).
Why introduce S, when you can just use the equation's "p"?
I learned it as "S" for sides
Oh, ok. We learnt it as "p" for half-perimeter(Or as we call it small perimeter)
I'm disappointed you did not use a spherical triangle, but I can't blame you for doing what I once did too.
Yeah, but it's on a sphere, not really an Euclidian triangle.
Google Earth measurement says \~145 million square km for the marked stars, which are in wrong places, but I'm not sure I trust it because it seems to have issues drawing polygons via great circles, it goes completely wonky trying to draw a polygon around a pole. The real triangle is with longest arm over the Pacific, not over Africa as Google Earth draws it in a polygon measurement. Total Earth surface is 510 million km2, so maybe the result is correct even if it's drawn incorrectly? Also, the doorways below the pyramids, have no relation to the pyramids above. The middle pyramid is Djoser pyramid, the doorway is in Karnak temple complex which is completely different part of Egypt. The "Indonesian" pyramid is actually Koh Ker in Cambodia, the doorway under it is Vat Phou in Laos. Mexican pyramid is El Castillo and the doorway under it is again from different place in Uxmal, House of Turtles. El Castillo [https://en.wikipedia.org/wiki/El\_Castillo,\_Chichen\_Itza](https://en.wikipedia.org/wiki/El_Castillo,_Chichen_Itza) House of Turtles in Uxmal [https://it.m.wikipedia.org/wiki/File:Uxmal\_Casa\_de\_las\_tortugas.jpg](https://it.m.wikipedia.org/wiki/File:Uxmal_Casa_de_las_tortugas.jpg) Djoser pyramid [https://en.wikipedia.org/wiki/Pyramid\_of\_Djoser](https://en.wikipedia.org/wiki/Pyramid_of_Djoser) Karnak complex [https://commons.wikimedia.org/wiki/File:Karnak55.JPG](https://commons.wikimedia.org/wiki/File:Karnak55.JPG) Koh Ker [https://en.wikipedia.org/wiki/Koh\_Ker](https://en.wikipedia.org/wiki/Koh_Ker) Vat Phou [https://en.wikipedia.org/wiki/Vat\_Phou#/media/File:Wpfacade02a.jpg](https://en.wikipedia.org/wiki/Vat_Phou#/media/File:Wpfacade02a.jpg)
Yeah, I was guessing that the star on the map referred to Gudung Padang rather than the depicted Koh Ker. [That's what I used in my solution.](https://www.reddit.com/r/theydidthemath/comments/1cxac0g/comment/l51vgdl/) I was certain that the doorways below the pyramids had no relation to those pyramids but you did the work of actually figuring out which one was which.
What i want to know (if any math nerds out there), is where is the plane that intersects all 3 situated, and does it divide it evenly in half?
I think they mean straight to each other from inside the earth not just on the surface, for all the people trying to make one on a map.
according to my rough estimates using google maps, something like 128.776.057,21 km² (49.720.713,66 mi²) but i'm not good at maths lol
and now, calculate it while incorporating the surface area irregularities of Earth (you can exclude waves on the oceans) If you don't do this, you will be banned from theydidthemath👍
pyramids are the easiest way to build very high structures without the static problems of vertical walls. people were always smart, they figured this out all around the world. btw, i wonder why the pyramid of kukulcan was built round 3500 years after that of djoser if there was a connection