Student Questions 9-23-14
Should we write a movie about 4-d safe stealing antics?
I won’t stop you.
What if a 5D being endcountered a 2D being?
Then the 2D being would see the level curves of the 5D being obtained by fixing w and
z to be constant.
Would a 5D being have similar properties to a 4D being as a 4D being does
to a 3D being?
There is no reason not to think so.
What is your favorite sit down restaurant?
If there is food I am happy. I don’t think I have a favorite.
What is the easiest way to identify 3D graphs?
With lots of experience and practice.
Can you make a comic strip about encountering a 4D being?
I am a pretty busy person and am not very artistic. You could read Spaceland.
Do you believe in 4D beings?
I don’t know. Are there 2D beings?
Any chance you can teach lectures too? You explain things very well.
Thank you but unfortunately I don’t have a Ph.D yet. Sometimes grad students teach
stand alone classes in the summer but that wouldn’t matter to you because you will be
passed calc 3.
Isn’t time the fouth dimension?
Spacetime is a 4 dimensional space that encorporates time but it is non-Euclidean and
behaves very differently from normal Euclidean space. Time should not be considered
the fourth Euclidean dimension. You should read the Wikipedia article on four
dimensional space.
Mathematically can we articulate movement in any dimension?
Of course. You should be able to write down the equation for a curve in any dimension.
Just make the vectors longer.
1
Find the equation of the plane that contains the point (3, 0, 5) and the line
h1, 0, −1i − th3, 7, −6i.
Ok well clearly h3, 7, −6i is the direction vector for the line and lies in the plane. I need
another vector in the plane that is not parallel to this vector. I will take the vector that
goes from the point (1, 0, −1) on the line to the point (3, 0, 5). This vector is h2, 0, 6i. So
crossing my two vectors in the plane I get that h42, −28, −14i is normal to the plane.
Using this vector and the point (3, 0, 5) I get that the plane is
42(x − 3) − 28y − 14(z − 5) = 0.
2