# Tagged Questions

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### Confusion with Bolyai-Gerwien theorem

The Bolyai-Gerwien theorem states: Given two polygons with the same area, it is possible to cut up one polygon into a finite number of smaller polygonal pieces and from those pieces assemble into ...
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### Beginning of Romance

I am a 17 guy from India. The fascination of maths has struck me recently, while I am in standard 12th. But all the resources I have, is some school textbooks. M.L Agrawal's of 11th and 12th. I don't ...
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### Prove the Gaussian curvature $K=0$

If two families of a geodesics on a surface intersect at a constant angle $\theta$, prove that the Gaussian curvature of the surface is zero, i.e. $K=0$. Please explain how to show the question. ...
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### Prove that the curves of the family $v^3/u^2=k$ are geodesics on a surface

Prove that the curves of the family $v^3/u^2=k$ where $k$ is a constant are geodesics on a surface with the metric $$v^2 \, du^2-2uv \, du+2u^2 \, dv^2$$ where $u,v \gt 0$.
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### Showing to be Unit-sphere

First and second fundamental forms are both $du^2 +\cos^2 u dv^2$ I want to show that the surface is a part of the unit sphere. What I did is following; $E=L=1$ $F=M=0$ $N=G=\cos^2 u$ ...
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### Geodesic eqautions and length of a curve in geodesic coordinate system.

About geodesic coordinates: Let S be regular surface. $p\in S$ $\gamma$ be unit speed geodesic on $S$ with parameter $v$ and $\gamma (0)=p$ $\tilde \gamma^v$ be unit speed geodesic s.t. ...
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### Geodesics on torus

Describe the geodesics on Torus $$\sigma (u,v)= ((a+b \cos u)\cos v, (a+b\cos u)\sin v, b\sin u)$$ First fundamental form for torus is $$b^2 du^2 +(a+b \cos u)^2dv^2$$ Consider unit-speed ...
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### Geodesics on spheroid

Describe the geodesics A Spheroid obtained by rotating the ellipse $\frac{x^2}{p^2}+\frac{z^2}{q^2}=1$ around the z-axis where $p, q\gt 0$ Please explain this question explicitly. Thank you:)
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### Geodesic equations and christoffel symbols

I want to learn explicitly proof of the proposition 9.2.3. Which books or lecture notes I can find? Please give me a suggestion. Thank you:)
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### Affine variety example.

I know how to show the statement. But I cannot find an example (the part I underlined by a yellow pen) please help me for finding an example. Note: For example, can I consider the following ...
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### Differential geometry question.

Please explain how to solve this question. Thank you:) And sorry for hand-writing.
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### Proving the Obvious

Is it normal that I have the hardest time when I'm trying to prove statements that are blatantly obvious on a visual and/or intuitive level? For instance, how does one go about formally proving the ...
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### I want a good dictionary of mathematics/ geometry

I noticed I a made a mistake in some geometrical terminology and wanted to better my life by buying a new dictionary of mathematics or more specialised Geometry. (okay I am just a shopaholic for ...
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### Show that the image of Gaussian map of a generalized cone is a curve on $S^2$ and deduce that the cone has zero Gaussian curvature.

Show that the image of Gaussian map of a generalized cone is a curve on $S^2$ and deduce that the cone has zero Gaussian curvature. I dont have enough idea. Please explain the question clearly. ...
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### Compute the geodesic curvature of any sphere on a sphere.

Compute the geodesic curvature of any sphere on a sphere. Again there exists its answer, but not understandable for me. Please explain it explicitly. Thank you so much. (If required, i can post ...
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### Second fundamental form question.

Honestly, I dont have any idea for that question I posted. Please can someone help me solving the question. Thank you.
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### The second fundamental form and isometry.

What is the effect on the second fundametal form of asurface of applying an isometry of $\Bbb R^3$ ? Or a dilation? I posted its answer. This answer is not understandable for me in general. ...
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### Question on Geometry

I have a B.Ed in Management, but recently developed interest in geometry & would love to study it on my own. Do i need or must have a B.A in Maths before doing this ?
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### Given a line segment. Construct an equilateral triangle with one side the given line segment.

I found this problem in a website, but I don't know how to solve it. Given a line segment $AB$. Construct an equilateral triangle with one side being $AB$.
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### Want to learn differential geometry and Riemannian geometry by myself

I want to follow a Ph.D. programme on geometric analysis. The main focus are Monge-Ampere equations and convex level set of $p$-harmonic equations. The theory of PDEs is very familar to me. However, I ...
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### The area problem!

We have to find area of the quadrilateral formed by joining the point of intersection of the four quarter circles that are drawn from each vertex in a unit square. $\hspace{4cm}$ The challenge is ...
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### What prerequisite material should I work through to understand four dimensional space?

I understand (at least to a comfortable degree) dimensions which are less than or equal to 3. For the past several years, I have been hearing a lot about four dimensional space. I'm intrigued and ...
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### Self-Teaching: Is Geometry the Nexus of all Mathematics?

Necessary prologue: I'd really like to become more fluent in the language of mathematics. I don't have a schedule that permits me taking a class and any on-line tutors that I find seem relatively ...