Questions tagged [geometry]
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For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
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Need help finding a formula for question that was solved by trial and error
The following question can be worked out by trial and error, but is there a formula that can be used? L shaped room has perimeter of 48m and area of 80m2. What is the length of each wall? geometry area- 1
Integral of angle between tangent and line
I have a problem like this but still haven't figured out how to solve it or what this concept is called in math. Let's say I have a continuous and differentiable curve $S: y=f(x)$ from $A$ to $B$. $L$ ... calculus geometry- 11
Show that $M :=\{J\in M_{2n}(\mathbb{R}); J^2 = -I\}$ is a submanifold of $M_{2n}(\mathbb{R})$
I want to show that: $$ M := \{J \in M_{2n}(\mathbb{R}) \mid J^2 = -I \} $$ is the submanifold of $M_{2n}(\mathbb{R})$, and I am given a hint to use Theorem 1. Theorem 1. Let $m,n,l \geq 0$. Suppose ... linear-algebra geometry differential-geometry manifolds geometric-topology- 31
If it exists, can a real tesseract appear to us in 3D space completely different than our analogue depictions?
It's a fact we as human beings cannot comprehend how an object looks like in spatial dimensions higher than 3. Yet, in mathematics we are able to project analogues of objects from incomprehensible ... geometry mathematical-physics projective-geometry projective-space dimension-theory-analysis- 11
What shape to cut sheet in order to perfectly cover a square pyramid with no overlaps? [closed]
I am making a tent using 4 bamboo sticks. I need to cut a cloth to fit over it perfectly but what shape should I cut the sheet when it is flat so it fits over this tent perfectly. The tent has height ... geometry problem-solving- 307
Pappos Theorem and distance of points
Let be $CDEB$ a parallelogramm. $F,G$ any points on the inner lines $DE$, $CB$ like in the picture. How can I show, that $CJ$=$KE$ ? I thought about using Pappos Theorem, which states, that $H$ and $... geometry- 989
Geometry - I am getting two different results when using two different scalar product properties
I am trying to solve a problem regarding the scalar product. The problem has multiple choices, and I solved it in two different ways, and got different values. Both of the values were a choice, but ... geometry trigonometry inner-products- 21
Similar triangles in pinhole camera
I am trying to understand how we concluded below that the two triangles in pinhole camera example below are similar? What rule we used to conclude they are similar please (AA, SAS, SSS)? Then we ... geometry- 1,071
Is it possible to prove that for any injective function $f: \mathbb{R} \to \mathbb{R}$ if $f(x)>f^{-1}(x)$ then $f(x)>x$?
So I just came up with this question in my brain, when thinking about that the inverse function has a graph that is symmetric to the original function's graph about the line $y=x$. Then if $f(x)>f^{... real-analysis geometry functions- 11
Fit rigid piecewise linear body to point cloud
I have a set of 3D points, each of which can be considered a point lying inside a rigid body of known dimensions. The actual object is straight cylindrical rods arranged as in the image below. The ... linear-algebra geometry 3d least-squares rigid-transformation- 11
Perpendicularity is not transitive
How to convince someone that if a plane (Pxy,P,Pz) is perpendicular to a plane (O,Px,Py) and the plane (Px,O,Py) is perpendicular to the plane (Px,Pxz,Pz) is not always true that (Pz,P,Pxy) is ... geometry vector-spaces metric-spaces euclidean-geometry- 11
Proving that $\angle MAC = 30^{\circ}$
In $\Delta ABC$, $M$ is an interior point such that, $MB=MA$, $MC=CB$, $\angle CBA = 2 \angle BAC$. Prove that $\angle MAC = 30^\circ$ I was able to solve this question using trigonometry here's my ... geometry euclidean-geometry triangles angle- 393
How to show that an ellipse is axially parallel
Let be $ f_1 (1,0) $ and $ f_2= (-1,0) $ and $ a>2 $ $E_a := \{ p \in \mathbb{R}^2 | || p - f_1 || + ||p- f_2 || = a \} $ How can I show (with the priciple of the Gardener's Construction maybe ?) ... geometry- 317
When an ellipse touches the sides of a triangle
An ellipse touches the sides of a triangle $abc$ from inside in the points $a',b',c'$. How can I prove, that the lines $ aa',bb',cc'$ meet in one point? The ellipse equation is : $ \frac{x^2}{a^2} + \... geometry- 131
$L(\mathbb{R}^n)$ is a metric space and $\Omega$ is open in $L(\mathbb{R}^n)$. How to image $\Omega$?
I am reading "Principles of Mathematical Analysis" by Walter Rudin. 9.8 Theorem Let $\Omega$ be the set of all invertible linear operators on $\mathbb{R}^n$. (a) If $A\in\Omega$, $B\in L(\... general-topology geometry- 6,235
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