Tagged Questions
2
votes
0answers
77 views
Imagining four or higher dimensions and the difference to imagining three dimensions
I’m very interested in how people envision four or higher dimensions.
And I’m especially interested in how geometers and topologists who actually work in four dimensions do.
Now I know of the video ...
2
votes
1answer
30 views
The best softwares to understand the intersections of the 3D objects in the Euclidean space
What is the best software (Easy to follow and clear graphics) to draw the intersections between two spheres, Two spheres and a pyramid, for example.
The centre and the radius of the spheres are given ...
5
votes
2answers
83 views
Why generalize the Euclidean metric?
It is well known that the Euclidean metric can be generalized to $\Bbb R^n$ by $\sqrt{(x_1-x'_1)^2+\cdots + (x_n-x'_n)^2}$, and that under this generalization it is still a metric and satisfies ...
4
votes
1answer
62 views
Geometric explanations of approximations of $\pi$
Does any fast modern algorithm for approximating $\pi$ have a geometric interpretation as $\int \sqrt{1 - x^2}$ does?
7
votes
2answers
234 views
Connection between algebraic geometry and high school geometry.
if there is one thing that going to math competitions has taught me it is that I suck at high school olympiad level geometry. However I often find solace in the fact that not a lot of mathematicians ...
1
vote
0answers
70 views
Draw curves and planes in latex [closed]
I want to submit a paper and the only thing that's left to do is to add some graphics.
My deadline is on Wednesday/Thursday.
What I want to do is some basic curve/plane drawings. Here is an image: ...
3
votes
4answers
299 views
Why do we draw the $xyz$ coordinate system like this?
Usually people (including, for instance, Calculus teachers) draw the $xyz$ coordinate system in such a way that the $y$ and $z$ axes are perpendicular to each other:
Imagine I actually got three ...
3
votes
4answers
114 views
What is a vector?
What is a vector?
As the question says what is a vector and what are its uses or, I mean, when should we use vectors?
Is this a branch of geometry or algebra or trigonometry?
4
votes
2answers
327 views
Geometric intuition behind gradient, divergence and curl
I learned vector analysis and multivariate calculus about two years ago and right now I need to brush it up once again. So while trying to wrap my head around different terms and concepts in vector ...
1
vote
1answer
113 views
Book recommendation request for geometric bodies (cube, pyramid, prism etc.)
Can anyone recommend books that deal with geometric bodies (cube, pyramid, prism etc.)?
I haven't been able to find any.
2
votes
3answers
118 views
Number of points on line segment
I know the line segment have a infinite number of points, but i know that exist different kinds of infinity ( $\aleph_0 $). My question is there same number of points on segment of line and entire ...
3
votes
0answers
50 views
Books on n-dimensional euclidian geometry?
Could anyone please recommend some books on n-dimensional Euclidean geometry? Thanks!
10
votes
2answers
237 views
What Mathematics questions can be better solved with concepts from Physics?
Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics ...
1
vote
2answers
49 views
What are some alternative ways of describing a Tetrahedron rather than using 4 points?
What are some alternative ways of describing a Tetrahedron rather than using 4 points?
This question made me wonder besides using the four points following methods could also be used to describe a ...
20
votes
4answers
1k views
What are the dangers of visual exposition of mathematics?
I've heard several times (such as this one) that it's dangerous to learn/prove/teach mathematics through images. I've also read somewhere that showing mathematics through images helps one's intuition ...
4
votes
4answers
243 views
Strategies for arranging coins in a circle
Suppose you have $n$ identical circular coins and you would like to arrange them on the table so that their edges touch and their centers lie on a circle.
Mathematically, there is no trouble. "Just" ...
10
votes
2answers
265 views
Elementary Geometry Nomenclature: why so bad?
A long-ish wall of text, and I apologize.
Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A ...
17
votes
6answers
769 views
I'm teaching a college geometry course. What should I cover?
I've been asked to teach "Foundations of Geometry" at the University of South Carolina. Apparently, professors in the past have all done very different things, and I have a lot of choice in the ...
2
votes
1answer
116 views
Why should coordinate transformations be reversible?
Intuitively I understand why coordinate transformation should be reversible. New coordinates should cover the same area covered by the initial coordinates, i.e. there should be one-to-one mapping.
...
11
votes
12answers
770 views
Explaining Horizontal Shifting and Scaling
I always find myself wanting for a clear explanation (to a college algebra student) for the fact that horizontal transformations of graphs work in the opposite way that one might expect.
For example, ...
1
vote
3answers
269 views
How to fill up the gap between a typical advanced undergraduate algebraic curve course and High school basic geometry/precalculus course?
Based on this question i asked recently: A question about geometry of plane curve books, i think it is too advance for a HS student/ typical second or third year undergraduate math majors to read on ...
12
votes
2answers
244 views
Does every closed curve contain the vertices of a square?
This is the question on Futility Closet
Is there really no answer?
2
votes
1answer
115 views
Intuition of projective plane and space
What is the geometric intuition of projective plane and space?
I can understand affine plane and 3 dimension affine space, for higher dimension, at least I can imagine it similarly as the 2,3 ...
11
votes
4answers
415 views
Implication and Interpretation of Banach Tarski
As I understand, the Banach-Tarski paradox says a ball in 3-space
may be decomposed into finitely many pieces and reassembled into two balls each of
the same size as the original. Despite being called ...
9
votes
5answers
815 views
The status of high school geometry
Okay, so we've all seen Euclidean geometry in primary and high school. Back then, I really thought of points as indivisible entities in space and lines as 'breadthless lengths'. As far as I could ...
0
votes
2answers
92 views
Is it possible to prove the uniqueness of a point in space?
Is it possible to prove the uniqueness of a point in space?
Well. I know this might be a silly question, but some response would be nice.
5
votes
3answers
272 views
Research in plane geometry or euclidean geometry
I was doing good at school in plane geometry and trigonometry - especially in geometric proofs like proving the equality of two line segments or two angles - more than I was doing in analytic ...
6
votes
4answers
367 views
Visual research problems in geometry
I am considering doing research in mathematics to be my career (and my life) someday.
I'm a visually oriented person in general , for example i prefer chess over cards because when i play chess i do ...
6
votes
3answers
348 views
Is there any good reason for a programmer to study geometry?
I'm a programmer and I've recently come back to math hoping to sharpen some of my skills. I did well in math in high school. I also did math competitively. I majored in music in college, so I stopped ...
1
vote
2answers
229 views
High-dimensionality and intuition
Over the years I've come across (usually as a tangential remark in a lecture) examples of how our intuitions (derived as they are from the experience of living in 3-dimensional space) will lead us ...
1
vote
0answers
47 views
References for implicit co-ordinates
When I was at school I learned about "implicit coordinates" for curves in a plane. Essentially these mapped the path in terms of arc length $s$ from a fixed point, and direction of travel $\psi$ ...
6
votes
0answers
317 views
Would you shake hands with Mickey Mouse? [closed]
I have two small children, and so I wind up watching a lot of children’s cartoons. A geometrical concept that leaps out at anyone who sees any significant amount of children’s cartoons is the ...
4
votes
2answers
188 views
Help finding solution for trigonometric equation
I have a mirror and a target. Given the sun's light angle of incidence, I must calculate how much to spin my mirror to hit the target with the light. The problem is shown in the following figure.
...
2
votes
3answers
388 views
How to prove the following inequalities?
thanks for your time. i am interested in various ways/techniques/tricks/methods (induction, convexity, concavity, maximum, minimum, geometry, trigonometry, ...) for proving the inequalities and their ...
1
vote
1answer
511 views
How to evenly distribute squares in a rectangular area?
Hi
i need to figure out how can i add given number of squares in a rectangle
i want to create this.
http://i.stack.imgur.com/MHoda.jpg
The whole scenario is to create a function that take a number ...
4
votes
2answers
221 views
How to analyze triangles in Lobachevsky geometry?
I got an assignment to prove certain things about right triangles in Lobachevsky geometry, but so far I don't know where to start. What model is the best for studying these objects? What is the ...
4
votes
4answers
554 views
Why does symplectic geometry have many applications in mathematics
It is not quite intuitive , at least from its origin. Could any one can give me an intuitive explanation?Thank you!
