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Mar
23
comment Geometry: Find angle x in triangle
Can you confirm the AB=CD statement?
Mar
23
comment Shifting RGB colors based on ratio
Convert RGB into HSV and compare the V values.
Mar
20
comment How many degrees of freedom does a line have on a plane?
Using $y=Ax+b$ not ok for planar geometry. Use $A x+ B y+ C=0$ instead to cover all the cases. This has the advantage that if a point $(P_x,P_y)$ lies on the line you can check easily with $A P_x + B P_y + C =0$. Although you use three coordinates, they are homogeneous because there is one extra since only two are needed to uniquely define all lines in the plane.
Mar
20
comment How many degrees of freedom does a line have on a plane?
A translation along the line does not change anything so there are only two transformations. Rotation and offseting.
Mar
20
comment How many degrees of freedom does a line have on a plane?
This implies three parameters (a,b,c) but this is not the minimum required. For example $x+y-1=0$ is equivalent to $2x+2y-2=0$. In fact, the above are called the three homogeneous coordinates of a line in the plane (just as there are 3 homogenous coordinatees of a point in a plane).
Mar
20
revised How many degrees of freedom does a line have on a plane?
added 139 characters in body
Mar
20
answered How many degrees of freedom does a line have on a plane?
Mar
18
revised Solve $Ux=y$ for $x$
Fixed typo where $x$ was typed as $y$.
Mar
18
comment Solve $Ux=y$ for $x$
The values of $x$ are incorrect. Check your work because your method is correct, overall. Specifically $x_1$ is incorrect.
Mar
18
revised Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
added 127 characters in body
Mar
18
answered Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
Mar
18
comment Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
Not that three terms of this series is by far much worse than 3 terms of a taylor series as presented in other answers. I wonder why this was accepted when its more complex and less accurate?
Mar
17
comment How can I interpret $2 \times 2$ and $3 \times 3$ transformation matrices geometrically?
The above A is not an orthonormal transformation because the 1st and 3rd columns are identical.
Mar
17
comment Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
Computer Algebra System : en.wikipedia.org/wiki/Computer_algebra_system
Mar
17
comment Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
I used a CAS for speed and accuracy. I see you went one up on terms. Well $f \approx \sqrt{x} \left(r+\frac{r^3}{8}+\frac{7r^5}{128}+\frac{33 r^7}{1024}+\frac{715 r^9}{32768} \right)$ with $r=y/x$.
Mar
17
answered Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
Mar
5
answered Calculate the radius of a circle given the chord length and height of a segment
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
Funny how math works correctly sometimes.
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
Did you read en.wikipedia.org/wiki/Tangent_half-angle_formula?
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
I added more details to the solution.