Here is my attempt to draw a diagram for this problem:
I'm confused about the "the perpendicular bisector of ##BC## cuts ##BA##, ##CA## produced at ##P, \ Q##" part of the problem.
How does perpendicular bisector of ##BC## cut the side ##CA##?
Hello,
I am studying geometry with an app on my phone. There was a difficult problem, which had two different explanations for solving. I correctly understood one explanation. I reviewed later without memory of the problem at all. There was an obvious attempt from what was learned previously...
In ##\mathbb{R}^2##, there are two lines passing through the origin that are perpendicular to each other. The orientation of one of the lines with respect to ##x##-axis is ##\psi \in [0, \pi]##, where ##\psi## is uniformly distributed in ##[0, \pi]##. Also, there are two vectors in...
I want to find the probability that the two points ($x_1, y_1$) and ($x_2, y_2$) lie on the opposite sides of a line passing through the origin $o = (0, 0)$ and makes an angle $\psi$ that is uniformly distributed in $ [0, \pi]$ with the $x$ axis when the angle is measured in clockwise direction...
Is the intersection of a 4D line segment and a 3D polyhedron in 4D a point in 4D, if they at all intersect? Intuitively, it looks like so. But I am not sure about it and how to prove it.
Hi,
I take a big number of disks to composed a circle of a radius of 1 m, the blue curved line is in fact several very small disks:
I take a big number of disks to simplify the calculations, and I take the size of the disks very small in comparison of the radius of the circle. The center A1...
A recipient (cube) of 1m³ is filled of small spheres, there are for example 1000³ spheres inside the recipient. There are also 1000³ elastics that attract the spheres to the bottom. The elastic are always vertical. One elastic for each sphere. One end of the elastic is fixed on a sphere and the...
I am unsure how to go about this. I tried following the suggestion blindly and end up with with some cumbersome terms that are not the answer. From what I understand the derivative at each point would equal to T?
Answer: I just can seem to get to this. I think I'm there but can't get it in...
Consider a point A outside of a line α. Α and α define a plane.Let us suppose that more than one lines parallels to α are passing through A. Then these lines are also parallels to each other; wrong because they all have common point A.
CONTEXT: We are finding the the buoyancy force on a boat which is upright in a still water (Fluid at rest) and the only gravity is acting as the external force. So, first we go for imaging a proper geometry of our boat.
See this figure :
For this figure the book writes:
Fig 8 represents...
Summary:: We have a rotating arm, offset from the centre of rotation by a certain length, which is controlled by varying the length of a control rod. Need the angle of the rotating arm in terms of length of the rod.
The blue line is a fixed column structure. CE and BD form the rotational...
So far all I can work out is that the angle of incidence of the outer two and inner two rays is zero degrees, however, I can't work out how to get started on the problem. I feel like I need to use vertical slowness rather than the normal snell's law since I'm working with a dZ rather than a dX...
Summary:: Suppose that [x, y] = e^{-3t} [-2, -1] is a solution to the system $x' = Ax$, where A is a matrix with constant entries. Which of the following must be true?
a. -3 is an eigenvalue of A.
b. [4, 2] is an eigenvector of A.
c. The trajectory of this solution in the phase plane with axes...
I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs in to begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant.
I recently watched a video by PBS infinite series...
Hello. I am confused with this matter that how should we write the transformation matrix for an expanding space. consider a spacetime that is expading with a constant rate of a. now normally we scale the coordinates for expansion which makes the transformation matrix like this:
\begin{pmatrix}...
Hello everyone!
I have been looking for a general equation for any regular polygon and I have arrived at this equation:
$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$
Where x is the side length and n the number of sides.
So I thought to myself "if the number of sides is increased as to almost look...
The metric for 2-sphere is $$ds^2 = dr^2 + R^2sin(r/R)d\theta^2$$
Is there an equation to describe the area of an triangle by using metric.
Note: I know the formulation by using the angles but I am asking for an equation by using only the metric.
Summary: Given three points on a positive definite quadratic line, I need to prove that the middle point is never higher than at least one of the other two.
I am struggling to write a proof down for something. It's obvious when looking at it graphically, but I don't know how to write the...
Honestly I don't know where to begin. I started differentiating alpha trying to show that its absolute value is constant, but the equation got complicated and didn't seem right.
I was able to find the equation of an ellipse where its major axis is shifted and rotated off of the x,y, or z axis. However, I could not find anywhere an equation for a spheroid that does not have its axis or revolution along the x,y, or z axis. How might I go about deriving such an equation...
I have tried a lot by angle chasing e.g. let ∠ABC=x° then ∠ACB=90°-x°. As AU=AV=radius of circle so ∠AUV=∠AVU=45°. I've connected U,D and V,D. Then ∠UDV=135° etc. But I haven't found any way to get near of proving AE=DE. I have also tried to prove 'the area of triangle AEU= area of triangle...
Through symmetry of parallelogram,I have come to this:
Here 1,2,3,4 denotes the area of the particular regions.Then I am stuck.Please help what to do next or whether there is any other way.
Homework Statement :[/B]
The following expression stands for the two angular bisectors for two lines :
\frac{a_{1}x+b_{1}y+c_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}}=\pm \frac{a_{2}x+b_{2}y+c_{2}}{\sqrt{a_{2}^{2}+b_{2}^{2}}}\qquad
Homework Equations
The equations for the two lines are :
##a_1x +...
Homework Statement
tl;dr: looking for a way to find the intersection of three cones.
I'm currently working with a team to build a Compton camera and I've taken up the deadly task of image reconstruction.
Background Theory:
https://en.wikipedia.org/wiki/Compton_scattering
For a single Compton...
Recently I started looking back at some basic mathematical principles, and I started thinking about the theorem of corresponding angles. It's such a basic idea that it seems obvious on an intuitive level, but despite that (or possibly because of that) I can't think of a good way to formally...