Really dumb question: why do we use e_i for unit vectors?

In summary: Maybe some people think that this is a clever little joke that math teachers like to play on unsuspecting students.
  • #1
Peeter
305
3
Anybody know the history of why something like [tex]\mathbf{e}_i[/tex] is conventionally used for unit vectors (as opposed to u for Unit which is less common).

I assume this originates from another language? If so I'm curious what language and what word.
 
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  • #2
German, I suspect - ein.
 
  • #3
Ah. One (unit). Thanks!
 
  • #4
I'd always been told it was short for "element."
 
  • #5
quadraphonics said:
I'd always been told it was short for "element."
Never believe what a math teacher tells you!
 
  • #6
D H said:
German, I suspect - ein.

I agree, "e" for "Einheitsvektor" meaning unit vector.

Might also be derived from Euclidean though..who knows for sure..:smile:
 
  • #7
HallsofIvy said:
Never believe what a math teacher tells you!

How come?
 
  • #8
sutupidmath said:
How come?
He's a math teacher trying to revive Epimenides paradox. Follow his advice: Don't believe anything he says.
 
  • #9
I am assuming he is implying with this, that we, students, must check everything out on our own, no matter who tells us that sth is true or not. We have to verify everything on our own, right, is this what halls is saying, right?

Ok, i am going to check the meaning of that paradox on wiki.
 
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  • #10
whats Epimenides paradox??
 
  • #11
transgalactic said:
whats Epimenides paradox??

google it!
 
  • #12
aaahhh i know that from the "SAT" exam

the lier paradox

those logic questions took a decade from my life
 
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  • #13
I actually found this discussion to be fairly informative. I never think that asking for historical reasons for notation is a stupid question.
 
  • #14
I should have labelled the post "non-technical question: ..." ;)
 
  • #15
why does this nonsense thread receive space? mindless relief?
 
  • #16
mathwonk said:
why does this nonsense thread receive space? mindless relief?
Would there be something wrong with that?
 
  • #17
Epimedes' paradox was to say that "All Cretan's are liars". Of course, Epimedes was himself a Cretan. There is, in fact, a place in the Bible (New Testament. I've forgotten exactly where but may be in Paul's epistle to the Corinthians) in which we are warned to beware of Cretans- "they say of themselves that they are liars"!
 

1. Why do we use e_i instead of just using i as a unit vector?

Using e_i as a unit vector is a convention that helps differentiate it from other variables. In mathematics and physics, i is commonly used to represent the imaginary number, so using e_i helps avoid confusion.

2. Is e_i the only notation used for unit vectors?

No, there are other notations that can be used for unit vectors, such as i-hat or x-hat. However, e_i is a widely accepted convention and is commonly used in mathematical and scientific contexts.

3. What does the subscript i in e_i represent?

The subscript i in e_i represents the specific coordinate or direction in which the unit vector is pointing. For example, e_x would represent the unit vector in the x-direction, and e_y would represent the unit vector in the y-direction.

4. Can e_i be used for any type of vector, or only for unit vectors?

e_i is typically used for unit vectors, which have a magnitude of 1. However, it can also be used for any vector that has a magnitude of 1, regardless of its direction.

5. How is e_i related to the concept of basis vectors?

e_i represents the unit vector in the direction of the i-th basis vector. Basis vectors are a set of linearly independent vectors used to define a coordinate system, and e_i is one of these basis vectors.

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