1
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2answers
43 views

Find the matrix that represents a rotation clockwise around the origin by$ 30∘$ followed by a magnification by a factor of 4.

Find the matrix that represents a rotation clockwise around the origin by 30∘ followed by a magnification by a factor of 4. My attempt: I multiplied the magnification matrix $\left[ ...
0
votes
0answers
39 views

Using basic transformations to derive matrix for the reflection in a line?

Using basic transformations (translation, scaling and rotations), show all the steps to derive the transformation matrix for the reflection of points n the line : y = 3 - x I know that a directional ...
1
vote
1answer
157 views

Finding equation of the image under a linear transformation

The equation of C is $x^2 + y^2 =1 $ How do I find the equation of the curve $C'=f(C)$ This is the image of $C$ under the linear transformation $f$ represented by the matrix $A=\begin{bmatrix}2 & ...
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0answers
78 views

Transforming FCC, BCC and HCP lattice types to cubes.

I was wondering if it is possible to transform the FCC, BCC and HCP into SC, or simple cubic lattices while preserving the lengths between the nodes? I would like to transform each into this: ...
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1answer
82 views

Images of Lines

I'm studying for this exam and one of the questions I am stuck on is: Find the image of the line $$3x-y+1 = 0$$ under the transformation $$z \mapsto \frac{2}{z+1}$$ So I know I have to convert the ...
2
votes
3answers
73 views

geometry: linear transformation

I know I do it wrong but where is the mistake??? In E3* are given the points $A(1,0,0,0)$, $B(0,1,0,0)$, $D(0,0,1,0)$, $O(0,0,0,1)$ and $E(1,1,1,2)$. The linear transformation $\Phi$ operates ...
1
vote
1answer
94 views

Set with plane having two axes of symmetry with angle of intersection

Proof that a closed and compact subset of plane having two axes of symmetry with angle of intersection not a rational multiple of $\pi$ is either a disc or a whole plane. Proof The composite of two ...
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1answer
198 views

transformation between square and a polygon?

I have a square and a polygon. I want to transform all the points inside this square such that they are mapped inside the polygon. I was trying using scale and rotate matrices but I am not able to ...
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1answer
1k views

Negative & Positive Shear Factor

My question relates to constructional geometry & matrices aren't to be involved in the solution because stated Math level is up to O Levels... The figure below shows shear with y=3 as invariant ...
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votes
1answer
281 views

What are spatial Transformations?

What are spatial Transformations? Are Affine transformations also part of spatial transformations?
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1answer
362 views

Finding reflection of a matrix

To 2 decimal places, what is the value of the lower-right entry in the reflection matrix $Q_a $if a = 1.05? Not even sure where to begin, is there a formula? This is what I could find in my textbook ...
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2answers
3k views

How can I determine the scale factor of a pantograph from the ratio of the arms?

I know this is probably simple but I just can't see it. How can I determine the scale factor of a pantograph from the ratio of the arms?
2
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0answers
129 views

Hyperbolic Universal Covering Space

I have been working with Ricci flow in the euclidean and hyperbolic space but have been having considerable trouble determining how to generate a universal covering space for complex hyperbolic ...
2
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0answers
339 views

How to find the center of an (scaled) ellipse?

This question is an extension of How to find the center of an ellipse?. The solution there works well, but in Javascript the floating point calculations are not that accurate. The workaround is to ...
3
votes
2answers
1k views

Rigid Motions - The product of two rotations around different points is equal to a rotation around a third point or a translation

I'm having some difficulty wrapping my head around rigid motions in a plane. In particular, I'm trying to solve this following problem: In a Euclidean plane, show that the product of two rotations ...