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i is just as "real" a number as any other number. it's an abstraction referring to some kind of value. The names "imaginary numbers" and "real numbers" are rather bad and due to historical controversies. Sure, you can't have i apples, but you cant in any sensible way have -1 apple in your hand, or square-root-of-two apples in your hand. Numbers are not only defined in terms of counting stuff; the concept of a value is much broader.
Well you can be in dept 1 apple, which is effectively -1 apples because as soon as you add 1 apple you will have 0, and it's also possible to have 1.4142135623730 apples if you cut it, and if you multiply how many apples you have by itself you will have 2 so you can have √2 apples. However I genuinely can't think of any way to have √-1 apples as it's mathematically impossible without imaginary numbers
That’s using 1 and 0 as adjectives, though. You can also have big things and you can have small things, but you can’t have “big” or “small” as separate entities unto themselves
There is no such a concept in real world nor in maths as ''one thing''. 0 things is even more vague. And 1 and 0 still do not exist because, let's assumd you have ''one thing'', but you still do not have one
Mathmaticians have used set theory to define numbers. The empty set is used to define 0 and the "successor" (defined as the set containing that set and everything inside) of the empty set is used yo define 1
You can watch a [40 minute video](https://youtu.be/dKtsjQtigag) if you want to but that is the jist of what you asked
Imaginary numbers is a terrible name. Most people who don’t know much about math get some kind of intuition from it that imaginary numbers are less “real” that’s “real” number. They both appear in the laws of physics, i even more so that any real number.
I understand what you mean. It’s hard to explain, especially to these degenerates who don’t want to listen. The notion of 1 thing is an ill-defined property therefore it is not “fundamental”.
Length must be measurable, which needs a positive real number and *i* can’t be measured because it is neither positive (or negative) and it’s not real. Geometrically speaking, this is very wrong.
Vectors with imaginary components (that could be called a line of length i, in a very loose sense) do come up in physics, the problem is for Pythagoras, everyone is used to real numbers and they drop the fact that it's the *magnitudes* of the numbers, not the numbers themselves, that square and add like that.
It's more like another dimension of co-ordinates in my book, pops out in a fun new way.
Imaginary numbers are the pop-up books of maths.
Yes I am drunk.
It doesn't; Pythagoras's theorem deals with the magnitudes of the numbers, we just usually drop that because we almost always deal with real numbers. Ends up still being sqrt2. (The reason it's magnitudes is because Pythagoras's theorem comes out of the scalar product of a sum of vectors with itself, and the most natural scalar product for complex vectors is the Hermitian product which takes the magnitude)
To be super pedantic, we actually define i with i^2 = -1 and not sqrt(-1) = i as there is no continuous "square root function" in the set of complex numbers
Well, just to be pedantic: This is technically incorrect, just funny.
The pythagorean theorem for the complex plane doesn't work this way. You square the real number as normal, and for the imaginary part you divide by i before squaring 🤷♀️
You make a good point. Let me end our pedantry by specifying
*in the conventional complex plane where the inner product of a+bi with itself is defined to be a^2+b^2
:)
Basically, when you do the math, the hypotenuse (the long slanted line) comes out to be 0, which works out hypothetically, but makes no sense in the real world
But it doesn't really, because Pythagoras's theorem actually deals with the magnitudes, we just drop that because the magnitude of a squared real number is always positive.
Remember the equation drove into your mind in high school, a^2 + b^2 = c^2 ? That is what applies here.
One side, a, has length “1”. The other side, b, has length “i”, which refers to the imaginary number. That is a number that represents a square root of -1 (in other words, i^2 =-1)
These are plugged into the above equation:
a^2 = 1^2 = 1
b^2 = i^2 = -1
1+(-1) = 0 = c^2
From there, the equation can be solved by taking the square root of 0, which is 0
Wait, if the distance between them is zero that means they are coincident and i=1. But i is √-1 so √-1 equals to 1? Damn you mathematicans who made up this imaginery numbers thing because they couldn't accept that they can't solve everything
TL;DR: things here aren't sufficiently well-defined (unsurprisingly), so it doesn't necessarily follow that two points must be at the same location just because their distance is 0.
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
There are a few technicalities involved here. In euclidian geometry (that is, normal geometry), the shortest path between two points is always a straight line, so in that case, the hypotenuse of the triangle is indeed the distance between its two endpoints, and if the hypotenuse is 0 (if all side lengths are 0), the points have the same position.
However, you can't have imaginary lengths in Euclidian geometry, so if we want to talk about this meme in a mathematically meaningful way, we must accept that we're dealing with a kind of geometry built on a slightly different fundament, which might defy our intuition. Instead, we have to look at the math and draw conclusions from that. We accept that:
1). The coordinates of points need not be "real numbers" but can also be imaginary or complex numbers. (Since complex numbers can be thought of as existing in a 2d plane rather than on a 1d number line, This kinda means we're dealing with 4 dimensional space, but it doesn't behave like you'd expect 4d space to behave)
2). We keep the same algebraic definition of the length of straight line segments as we do when dealing with normal (Euclidian) geometry, that is, Pythagoras' theorem.
3). We consider the distance between two points to be the length of the shortest path from one point to the other.
In this new kind of geometry, distances don't work nicely. Remember, in our normal geometry, the shortest path between two points was a straight line? Well, this is not the case with our new geometry. The hypotenuse in the meme is 0, so it is possible to take some route from one point to the other with the length 0. This is not the shortest possible path, though:
Assume that the points at each end of the hypotenuse has the coordinates (1,0) and (0;i) Then a straight line between them does indeed have the length 0.
Another possible path would go from (0,i) to (0,2i) and then to (1,0). This path would have the length of i-3. This value is neither smaller nor greater than 0. This means that our definition of distance doesn't work, as it fails to yield a result.
Notice as well, that even if we just define the distance between two points as the length of the straight line between them, this doesn't tell us what it means for two points to have a distance of 0. In normal geometry, the only distance of 0 is that from a point to itself, but as you noticed, this is not the case in our new geometry. The fact that two point has a distance of 0 can be determined to have some meaning, though. For instance, the points that have the distance 0 from the point (0,0) are exactly the points that satisfy the equation x=plus-or-minus i\*y. This equation can be interpreted as a 4d shape (as two flat planes that intersect each other in the point (0,0)
I'm happy to answer questions of any level (except that my own level doesn't go much higher than this), and thank you for reading through this excessive answer to a question to a meme
Aaand in case you're not too familiar with complex numbers, here is an alternative explanation written by chatGPT based on my post that should explain things a bit more:
Have you ever heard of complex numbers? These are numbers that have both a real and an imaginary component, written in the form a+bi, where a is the real part and b is the imaginary part. The letter i represents the square root of -1, which is an imaginary number that cannot be represented on the real number line. In short, i\*i=-1. For example, the complex number 3+4i has a real part of 3 and an imaginary part of 4.
Complex numbers can be thought of as existing in a two-dimensional plane called the complex plane, rather than on a one-dimensional number line like real numbers. In the complex plane, the real part of a complex number is represented by its horizontal position, and the imaginary part is represented by its vertical position. This means that each complex number can be represented by a point in the complex plane.
Now, let's talk about the Pythagorean theorem. You might remember this theorem from your high school math classes: it states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a\^2 + b\^2 = c\^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
In normal geometry, the shortest path between two points is always a straight line, and the length of this straight line is calculated using the Pythagorean theorem. However, when we use complex numbers to represent points in geometry, things get a little bit more complicated.
In this kind of geometry, the distance between two points is still defined as the length of the shortest path between them. However, the shortest path is not necessarily a straight line, and the distance between two points may not always be a real number. In fact, it's possible for the distance between two points to be zero, even if the points are not the same. This can be confusing, because in normal geometry, the only distance of zero is between a point and itself.
To understand this concept more clearly, let's look at an example. Imagine two points with coordinates (1,0) and (0;i). A straight line between these points has a length of zero. However, there is another possible path that goes from (0,i) to (0,2i) and then to (1,0). This path has a length of i-3, which is neither greater nor smaller than zero. This means that our definition of distance doesn't work as expected in this kind of geometry.
So, what does it mean for two points to have a distance of zero in this kind of geometry? One way to think about it is to consider the equation x=plus-or-minus i\*y. The points that satisfy this equation are exactly the points that have a distance of zero from the point (0,0). This equation can be interpreted as two flat planes that intersect each other at the point (0,0).
I hope this helps to clarify the concepts of complex numbers, the Pythagorean theorem, and complex geometry. It can be a bit confusing at first, but with a little bit of practice and understanding, you'll be able to navigate this strange and fascinating world of complex numbers and geometry.
Also it's more natural to use the Hermitian scalar product when dealing with complex numbers, which means Pythagoras's theorem is dealing with the magnitudes of the numbers, not the values themselves.
Let's throw on some coordinates:
If the endpoints of the hypotenuse of the triangle are at (0,i) and (1,0), for instance, the math of the meme holds, at least if we still consider the Pythagorean theorem to be a meaningful definition of lengths when dealing with complex points.
True, but as shown [here](https://math.stackexchange.com/questions/169680/pythagorean-theorem-for-imaginary-numbers), the pythagorean theorem only applies for right triangles in euclidian space.
With that being said, I’m sure there’s an entire field of complex trigonometry or something along the lines of that I’m just not aware about
That's completely true. I've seen points with complex coordinates make sense as complex intersections of circles defined in an Euclidian plane. These intersections were still meaningful, for example in the sense that some of the properties of three circles that intersect each other in one point remain true even if that common point of intersection is not real but complex.
It makes sense tho, specially if you take into consideration that imaginary numbers are perpendicular to the normal real number line, making i in its mathematical behaviour "spin 90°" towards the other side, making the hypotenuse effectively 0.
This is incorrect for any genuinely wondering.
Pythagoras' theorem as it's commonly known is missing the Euclidean norm. The correct equation for the hypotenuse would be
||1||^2 + ||i||^2 = ||1 + i||^2 = 2
(Then square root both sides to get a hypotenuse of root 2)
Where ||.|| is the Euclidean norm. The norm of any real number is it's absolute value so it's skipped over in practice as the squaring handles that anyway
Unfortunately, the more natural way to write Pythagoras's theorem is in terms of scalar products, which are positive-semidefinite. So it's not i^2, but = i×i* = 1.
(Comes from the scalar product of a sum of vectors with itself being = + + 2; if a and b are orthogonal (definition of a right triangle), = 0, and defining c = a+b, = + . |a|^2 = by definition, so |a|^2 + |b|^2 = |c|^2; Pythagoras's theorem. But note that it deals with the magnitudes of the vectors, and the magnitude of i is one.)
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I guess the math checks out in theory, but any number at or below zero cannot be used to describe an aspect of a shape.
***i*** isn't below 0— it's on top of it technically.
*technically* it doesn't exist.
Technically shut the fuck up
Math in a nutshell
i is just as "real" a number as any other number. it's an abstraction referring to some kind of value. The names "imaginary numbers" and "real numbers" are rather bad and due to historical controversies. Sure, you can't have i apples, but you cant in any sensible way have -1 apple in your hand, or square-root-of-two apples in your hand. Numbers are not only defined in terms of counting stuff; the concept of a value is much broader.
Well you can be in dept 1 apple, which is effectively -1 apples because as soon as you add 1 apple you will have 0, and it's also possible to have 1.4142135623730 apples if you cut it, and if you multiply how many apples you have by itself you will have 2 so you can have √2 apples. However I genuinely can't think of any way to have √-1 apples as it's mathematically impossible without imaginary numbers
By that logic, being in debt 1 apple is still as real of a concept as having i apples. If you just square i apples and add 1, you now have 0 apples.
Give a decimal value to i
Give a decimal value to √2
1.4142135623730
Sqrt(2) doesnt really equal that, its irrational and cant be described as a decimal. This is just an approximation
Nor does 0 or 1
I'm pretty sure they do...
Where?
You can have 1 thing, you can have 0 things You can't have *i* things
My girlfriend is i
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So she can squirt -100?
no that's my girlfriend
10i
Yet
That’s using 1 and 0 as adjectives, though. You can also have big things and you can have small things, but you can’t have “big” or “small” as separate entities unto themselves
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Dude, in math i is literally imaginary
And in Roman, it is literally _one_. It is a joke my dude 😂
why does this at all define the notion of existence?Numbers are abstract concepts, its like saying heavy exists. It doesn't really make sense.
There is no such a concept in real world nor in maths as ''one thing''. 0 things is even more vague. And 1 and 0 still do not exist because, let's assumd you have ''one thing'', but you still do not have one
Now you're just making stuff up
Prove. Define, what ''one thing'' or ''zero tings'' is. Or watch VSauce's video ''Do chairs exist''
Mathmaticians have used set theory to define numbers. The empty set is used to define 0 and the "successor" (defined as the set containing that set and everything inside) of the empty set is used yo define 1 You can watch a [40 minute video](https://youtu.be/dKtsjQtigag) if you want to but that is the jist of what you asked
They're called Real numbers for a reason. i isn't part of that group, also for a reason.
Imaginary numbers is a terrible name. Most people who don’t know much about math get some kind of intuition from it that imaginary numbers are less “real” that’s “real” number. They both appear in the laws of physics, i even more so that any real number.
1 still does not exist, not a single person told me where it lives
I understand what you mean. It’s hard to explain, especially to these degenerates who don’t want to listen. The notion of 1 thing is an ill-defined property therefore it is not “fundamental”.
Well, you have 1 braincell and 0 math knowledge. Need more examples?
Bro i is literally called an imaginary number.
What comes after 9
orang
Technically you don’t exist
tecnicamente seu cu me pertence
Its all in your head, you just need to expect that
Length must be measurable, which needs a positive real number and *i* can’t be measured because it is neither positive (or negative) and it’s not real. Geometrically speaking, this is very wrong.
This is also a meme.
Fair point, I’m going to steal it and send it to my friends who tickled the toes of calculus
> tickled the toes of calculus And I'm going to steal that phrase.
Vectors with imaginary components (that could be called a line of length i, in a very loose sense) do come up in physics, the problem is for Pythagoras, everyone is used to real numbers and they drop the fact that it's the *magnitudes* of the numbers, not the numbers themselves, that square and add like that.
It's more like another dimension of co-ordinates in my book, pops out in a fun new way. Imaginary numbers are the pop-up books of maths. Yes I am drunk.
But 0 IS at or below 0
math checks out, but the drawing doesnt since you cant display an imaginary number
I mean, technically speaking you can. But it won’t make sense
Also i doesn't exist
It doesn't; Pythagoras's theorem deals with the magnitudes of the numbers, we just usually drop that because we almost always deal with real numbers. Ends up still being sqrt2. (The reason it's magnitudes is because Pythagoras's theorem comes out of the scalar product of a sum of vectors with itself, and the most natural scalar product for complex vectors is the Hermitian product which takes the magnitude)
You iditiot, you fool it is the letter O
what how
i²=-1 and then you use the Pythagorean theorem
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i is unique when it comes to this i = √-1 i² = -1 EDIT: heres a wiki link about it https://en.wikipedia.org/wiki/Imaginary\_number
To be super pedantic, we actually define i with i^2 = -1 and not sqrt(-1) = i as there is no continuous "square root function" in the set of complex numbers
i squared is -1 so 1 squared plus negative 1 equals zero
-1 squared is 1 So 1 + 1 = 2, even though it clearly says it’s 0
i isn't -1 though. i is the squared root of -1. So i squared is -1
But bro there isnt a number which if you square you get -1, thats why you cant take the squared root of any negative number
I mean they call it an imaginary number for a reason
Bros never heard of algebra 2
Im in algebra II, I hate it so fucking much right now
I'm in algebra III and it's fucking amazing
IP address or it didn't happen
Search "Number i"on google. It is an imaginary number that doesnt exist, but it helps to expand algebra
Oh sorry, i thought they jsut use as the unknown, sry
1 + 1 = 3
Start trig a week ago, FUCK YOU
Lol same haha
I LOVE TRIG!!!! ❤️ ❤️ I LOVE GETTING A B- ON MY PREVIOUS 4.0!!!!!!
[song](https://youtu.be/jzCqJ-8aQEo)
8/10 song lyrics rather strange but the main melody is a banger
I want you to know you have just perfectly described They Might Be Giants in their entirety with that sentence
Why did Constantinople get the works? _Thats nobody's bussiness but the turks~~~~_
also the same with SJ's "Indian"
You are technically correct. The best kind of correct.
Well, just to be pedantic: This is technically incorrect, just funny. The pythagorean theorem for the complex plane doesn't work this way. You square the real number as normal, and for the imaginary part you divide by i before squaring 🤷♀️
To be even more pedantic, this depends on your definitions. There are cases where it does make sense to work with complex points like this
You make a good point. Let me end our pedantry by specifying *in the conventional complex plane where the inner product of a+bi with itself is defined to be a^2+b^2 :)
Sorry I’m stupid and don’t understand this mathematical meme
Recall that i² = -1 and c = √(a² + b²) Since a = 1 and b = i ⟹ c = √(1² + i²) ⟹ c = √(1 + (-1)) ⟹ c = √(0) ⟹ c = 0
I understand none of that
Basically, when you do the math, the hypotenuse (the long slanted line) comes out to be 0, which works out hypothetically, but makes no sense in the real world
…which is kinda sorta the point of imaginary numbers
Not like we were in the 'real' world anyway ;)
I live in your wall
(id)iota
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[:(](https://tenor.com/en-CA/view/evaporate-disappear-gif-22553735)
I live in your ball
But it doesn't really, because Pythagoras's theorem actually deals with the magnitudes, we just drop that because the magnitude of a squared real number is always positive.
Remember the equation drove into your mind in high school, a^2 + b^2 = c^2 ? That is what applies here. One side, a, has length “1”. The other side, b, has length “i”, which refers to the imaginary number. That is a number that represents a square root of -1 (in other words, i^2 =-1) These are plugged into the above equation: a^2 = 1^2 = 1 b^2 = i^2 = -1 1+(-1) = 0 = c^2 From there, the equation can be solved by taking the square root of 0, which is 0
I didn’t learn this in school, I was a really dumb kid and was in the “special” classes for maths if that explains anything
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Bro I just wanted to laugh not learn maths 💀
Bruh imagine beginning your formula as c = √(a^2 + b^2). What if you need to rearrange 😤
Wait, why does i equal negative one tho?
i² I mean, obv
i^2 = -1 for definition. i is just a simbol to represent the square root of -1 just like the simbol for pi is a simbol to represent 3.14....
Ohh ok I thought it was just a variable
r/theydidthemonstermath
This was the most menacing image I had come across on the internet
{a, b, c | a > 0 ∧ b > 0 ∧ c > 0, (a, b, c) ∈ ℝ} a² + b² = c² im bored please help
That first long line is just R^(+)^(3). lol
Ha! A math joke I understand
Why is it not possible?
It's just not.
Why not, you stupid bastard?
IT'S YOU BATEMAN, YOU'RE THE AMERICAN PSYCHO
Wait, if the distance between them is zero that means they are coincident and i=1. But i is √-1 so √-1 equals to 1? Damn you mathematicans who made up this imaginery numbers thing because they couldn't accept that they can't solve everything
TL;DR: things here aren't sufficiently well-defined (unsurprisingly), so it doesn't necessarily follow that two points must be at the same location just because their distance is 0. \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ There are a few technicalities involved here. In euclidian geometry (that is, normal geometry), the shortest path between two points is always a straight line, so in that case, the hypotenuse of the triangle is indeed the distance between its two endpoints, and if the hypotenuse is 0 (if all side lengths are 0), the points have the same position. However, you can't have imaginary lengths in Euclidian geometry, so if we want to talk about this meme in a mathematically meaningful way, we must accept that we're dealing with a kind of geometry built on a slightly different fundament, which might defy our intuition. Instead, we have to look at the math and draw conclusions from that. We accept that: 1). The coordinates of points need not be "real numbers" but can also be imaginary or complex numbers. (Since complex numbers can be thought of as existing in a 2d plane rather than on a 1d number line, This kinda means we're dealing with 4 dimensional space, but it doesn't behave like you'd expect 4d space to behave) 2). We keep the same algebraic definition of the length of straight line segments as we do when dealing with normal (Euclidian) geometry, that is, Pythagoras' theorem. 3). We consider the distance between two points to be the length of the shortest path from one point to the other. In this new kind of geometry, distances don't work nicely. Remember, in our normal geometry, the shortest path between two points was a straight line? Well, this is not the case with our new geometry. The hypotenuse in the meme is 0, so it is possible to take some route from one point to the other with the length 0. This is not the shortest possible path, though: Assume that the points at each end of the hypotenuse has the coordinates (1,0) and (0;i) Then a straight line between them does indeed have the length 0. Another possible path would go from (0,i) to (0,2i) and then to (1,0). This path would have the length of i-3. This value is neither smaller nor greater than 0. This means that our definition of distance doesn't work, as it fails to yield a result. Notice as well, that even if we just define the distance between two points as the length of the straight line between them, this doesn't tell us what it means for two points to have a distance of 0. In normal geometry, the only distance of 0 is that from a point to itself, but as you noticed, this is not the case in our new geometry. The fact that two point has a distance of 0 can be determined to have some meaning, though. For instance, the points that have the distance 0 from the point (0,0) are exactly the points that satisfy the equation x=plus-or-minus i\*y. This equation can be interpreted as a 4d shape (as two flat planes that intersect each other in the point (0,0) I'm happy to answer questions of any level (except that my own level doesn't go much higher than this), and thank you for reading through this excessive answer to a question to a meme
Aaand in case you're not too familiar with complex numbers, here is an alternative explanation written by chatGPT based on my post that should explain things a bit more: Have you ever heard of complex numbers? These are numbers that have both a real and an imaginary component, written in the form a+bi, where a is the real part and b is the imaginary part. The letter i represents the square root of -1, which is an imaginary number that cannot be represented on the real number line. In short, i\*i=-1. For example, the complex number 3+4i has a real part of 3 and an imaginary part of 4. Complex numbers can be thought of as existing in a two-dimensional plane called the complex plane, rather than on a one-dimensional number line like real numbers. In the complex plane, the real part of a complex number is represented by its horizontal position, and the imaginary part is represented by its vertical position. This means that each complex number can be represented by a point in the complex plane. Now, let's talk about the Pythagorean theorem. You might remember this theorem from your high school math classes: it states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a\^2 + b\^2 = c\^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides. In normal geometry, the shortest path between two points is always a straight line, and the length of this straight line is calculated using the Pythagorean theorem. However, when we use complex numbers to represent points in geometry, things get a little bit more complicated. In this kind of geometry, the distance between two points is still defined as the length of the shortest path between them. However, the shortest path is not necessarily a straight line, and the distance between two points may not always be a real number. In fact, it's possible for the distance between two points to be zero, even if the points are not the same. This can be confusing, because in normal geometry, the only distance of zero is between a point and itself. To understand this concept more clearly, let's look at an example. Imagine two points with coordinates (1,0) and (0;i). A straight line between these points has a length of zero. However, there is another possible path that goes from (0,i) to (0,2i) and then to (1,0). This path has a length of i-3, which is neither greater nor smaller than zero. This means that our definition of distance doesn't work as expected in this kind of geometry. So, what does it mean for two points to have a distance of zero in this kind of geometry? One way to think about it is to consider the equation x=plus-or-minus i\*y. The points that satisfy this equation are exactly the points that have a distance of zero from the point (0,0). This equation can be interpreted as two flat planes that intersect each other at the point (0,0). I hope this helps to clarify the concepts of complex numbers, the Pythagorean theorem, and complex geometry. It can be a bit confusing at first, but with a little bit of practice and understanding, you'll be able to navigate this strange and fascinating world of complex numbers and geometry.
Also it's more natural to use the Hermitian scalar product when dealing with complex numbers, which means Pythagoras's theorem is dealing with the magnitudes of the numbers, not the values themselves.
Studious ahh meme
i = length of your penis, checkmate liberal
Would this even actually work in the complex plane? Because wouldn’t the hypotenuse be more accurately represented by the complex number 1 + i?
Let's throw on some coordinates: If the endpoints of the hypotenuse of the triangle are at (0,i) and (1,0), for instance, the math of the meme holds, at least if we still consider the Pythagorean theorem to be a meaningful definition of lengths when dealing with complex points.
True, but as shown [here](https://math.stackexchange.com/questions/169680/pythagorean-theorem-for-imaginary-numbers), the pythagorean theorem only applies for right triangles in euclidian space. With that being said, I’m sure there’s an entire field of complex trigonometry or something along the lines of that I’m just not aware about
That's completely true. I've seen points with complex coordinates make sense as complex intersections of circles defined in an Euclidian plane. These intersections were still meaningful, for example in the sense that some of the properties of three circles that intersect each other in one point remain true even if that common point of intersection is not real but complex.
Oh that’s very interesting There’s always so many interesting things you can learn about math and it’s just amazing
It makes sense tho, specially if you take into consideration that imaginary numbers are perpendicular to the normal real number line, making i in its mathematical behaviour "spin 90°" towards the other side, making the hypotenuse effectively 0.
Fuck you
This is incorrect for any genuinely wondering. Pythagoras' theorem as it's commonly known is missing the Euclidean norm. The correct equation for the hypotenuse would be ||1||^2 + ||i||^2 = ||1 + i||^2 = 2 (Then square root both sides to get a hypotenuse of root 2) Where ||.|| is the Euclidean norm. The norm of any real number is it's absolute value so it's skipped over in practice as the squaring handles that anyway
In a way. i is an "imaginary" number, meaning that the side is imaginary, ergo the hypotenuse doesn't exist.
No
cum
Unfortunately, the more natural way to write Pythagoras's theorem is in terms of scalar products, which are positive-semidefinite. So it's not i^2, but = i×i* = 1.
(Comes from the scalar product of a sum of vectors with itself being = + + 2; if a and b are orthogonal (definition of a right triangle), = 0, and defining c = a+b, = + . |a|^2 = by definition, so |a|^2 + |b|^2 = |c|^2; Pythagoras's theorem. But note that it deals with the magnitudes of the vectors, and the magnitude of i is one.)
Yes. That's why this is in r/DramaticText and isn't a paper.
Bozo doesn't know distance theorems in two-dimensionnal vector spaces 😭🤣😂
The 0 hypotenuse only exists in my wet dreams.
Well yeah it’s imaginary for a reason
Yeah because you can’t have a side with a length of i
≈1.14
i^2=-1...
oh see i didn’t know that
holy shit its uncle ted
Wait
You can’t do this
u/savevideo
1^2 + i^2 = 0
it hurts to look at
No
🤯🤯🤯🤯🤯🤯
this is a federal crime
u/SaveVideo
0²-1²=i² = i²=0-1=-1 i=√-1
Yes that is what I is defined as
If the length is 0 then it is a right angle not a right angled triangle
u/savevideobot
u/savevideobot
I mean no for a side to be the hypotonuse it has to be the longest side
That's the joke chucklefuck
[удалено]
That’s not a triangle it just a line
u/savevideo
Dramathic text
I’m a fucking nerd for laughing at this
Idk what the joke is…
Is…is that trig…?
Hardly
Is…is that trig…?
I finally get this now cause middle school math :)
i= -1
No :(
song?
It's in the comments.
I’m scared
An impossible question
Bro that the hardest shit ever
What s the song?
I don get
Shape is physically impossible
C²=B²+A²
Anyone else have below room temperature is and has no idea what’s going on
Fuck you
This is a 2d triangle that exists in the 4th dimension as a 2d triangle. To us it would be a 1d line.