# Tagged Questions

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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### calculate arbitrary points from a plane equation

I understand how one can calculate a plane equation (ax+by+cz=d) from three points but how can you go in reverse? How can you calculate arbitrary points from a plane equation?
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### Find the triangle with the greatest area using trigonometric ratios

The hypotenuse, c, of right $\triangle$ABC is $7.0$cm long. A trigonometric ratio for angle $A$ is given for four different triangles. Which of these triangles has the greatest area? a) sec $A$ = ...
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### A geometric inequality about the internal besectors [closed]

prove that in every triangle the following inequality is hold: $$\frac{1}{w_\alpha}+\frac{1}{w_\beta}+\frac{1}{w_\gamma}\le \frac{2}{\sqrt{3}}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$$ ...
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### Recommend guide book of algebraic geometry [duplicate]

I have a little knowledge about geometry and algebraic topology . I want to learn some basic conception and thought of algebraic geometry. Besides , I want to know main of theory of sheaves. What book ...
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### Geometrical Interpretation of Tensors (intuition)

How would one describe to a non-mathematician (an undergraduate physicist actually- so please do use mathematics-i am not even sure if they can be described without mathematics!) what do tensors ...
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### How do i compute how much i can rotate my tool?

I am at moment trying to implement an Ball tracker for a robot arm with a stereo camera monted on it as its tool. Illustration: http://m.imgur.com/5oojXdh The camera provide me with an dx, dy, dz ...
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### Find the other 2 interior angles of pentagon inscribed in a circle given 3 angles.

Given a pentagon $ABCDE$ inscribed in a circle with centre $O$. Three of the interior angles are $95^°$, $130^°$ and $138^°$. Find angle $x$ and $y$. I'm quite sure that $x$ and $y$ can be found as ...
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### How to find the correct value of pi? [duplicate]

Pi is defined as the ratio of $\frac{c}{r}$. Many ancient scintist try to find the value of pi. Some of the values are $\frac{22}{7}$(good hold upto 10 decimal point), $\frac{355}{113}$ (good hold ...
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### Construction of an $n$-Sphere

I have been thinking about various ways to construct an $n$-sphere. Starting with $S^2$, we can construct it by taking two disks, lifting the "meat" of the disks into a third dimension and then ...
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### Why does $\left(\frac b2\right)^2$ "geometrically complete the square?

I was just reading this MathisFun article on completing the square. It states that geometry can help complete the square. It starts off with a square and a rectangle (pictures come from link): ...
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### Intersecting three rays and a sphere of known radius

So I actually solved this problem using an iterative solver, but it annoys me because as far as I can tell it should be possible to do it directly. I have three known 3D "rays" that all start at the ...
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### How to solve this geometry problem which involves triangles and triangulation

I need to solve this trig problem. Can you please help me? Based on this image: I need to calculate $PO$ based on the values of $\alpha$, $\beta$ and $AB$ ( Assume that I know the values of ...
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### If point (cos(theta),sin(theta)) does not fall in the angle btw the lines y=|x-1| in which the origin lies then find the interval which theta belong

I don't get what is the condition for a point to lie between acute or obtuse angled region of two intersecting lines
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### Geometry, Intersection of Spheres

Can someone explain why the intersection of the unit sphere centred at (0,0,0) an the unit sphere centred at (1,0,0) is a circle of radius $\frac{\sqrt3}{2}$ in the plane {$x_1$=1/2}, centred at ...
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### Is the simplicial join of two spherical simplicial complexes itself spherical?

I think this ought to be true, but I am struggling to see why. Of course if one of the spheres is $S^0$ then this is trivially true, as we are just glueing two cones along their boundary. I'm not ...