Recent questions in Geometry

Polygons
Answered

Adrien Jordan
2022-09-27

I just want to make sure that the following algorithm is correct for computing the Minkowski difference of two shapes A,B:

$\text{Minkowski}(A,B)=\text{CH}\{x:x=a-b\text{for}a\in A,b\in B\}$

Where CH(S) is the convex hull of the set S and a,b are the vertices of the two polygons.

Geometric Probability
Answered

Sara Fleming
2022-09-27

Bernoulli's, Binomial, Geometric, Hypergeometric, Negative binomial, Poisson's, Uniform, Exponential, Normal, Gamma, Beta, Chi square, Student's distribution.

I would like to know how and when to use each of these distributions when solving problems in probability. If possible, make analogy with combinatorics (when we use permutations, variations and combinations).

Geometric Probability
Answered

mydaruma25
2022-09-27

Compute $p(x)\text{}\text{for}\text{}x=0,1,2,3,4,5$. (Hint: the formula for summing a geometric series will help you expand the denominator)."

Distance Formula
Answered

Medenovgj
2022-09-26

Coordinate Geometry
Answered

Kody Whitaker
2022-09-26

Distance Formula
Answered

mundocromadomg
2022-09-26

Angle theorems
Answered

Averi Fields
2022-09-26

Geometric Probability
Answered

Marcus Bass
2022-09-26

Inside a square of side 2 units , five points are marked at random. What is the probability that there are at least two points such that the distance between them is at most $\sqrt{2}$ units?

Indirect Proof
Answered

Medenovgj
2022-09-26

We have

$\sum _{j=1}^{n}\frac{1}{{Q}^{\prime}({\alpha}_{j})}=0.$

Do we have a proof relying on rudimentary techniques?

Finding volume
Answered

gaby131o
2022-09-25

I'm having an issue with a probability problem concerning solutions.

Assume there is an "observational region" in a dilute solution with a volume V, and as solutes move across its boundary, the number N of solute molecules inside the observation region fluctuates.

Divide V into M regions of volume v each with n particles. The solution is dilute enough that $n=0$ or 1 (there is no v with more than one particle of solute), and each cell is occupied ($n=1$) with probability $p=({\rho}_{0})v$.

If W(N) is the number of configurations of the observation volume when N solutes are present, what is the probability P(N) of observing a given value of N, in terms of p,W(N),M, and N.

I know the probability $P({n}_{1},{n}_{2},\dots ,{n}_{M})$ of finding the system in a particular configuration in the observation volume is $p(N)={p}^{N}(1-p{)}^{M-N},$, (Bernoulli Distribution), and since there are N particles in M spaces then the maximum number of configurations is $\frac{M!}{(N!(M-N)!)}$

I'm not sure where to go from here.

Finding volume
Answered

tarjetaroja2t
2022-09-25

I have been trying to solve this problem of finding the 'n-volume' of a paralleletope spanned by m vectors, where clearly $m\le n$. In general, for computational purposes, what I have managed to do is define volume as the product of absolute values of vectors obtained by gram-schmidt orthogonalizationn. (Makes sense right? That's the natural interpretation when we say volume)

I had to do two things, firstly to show that this definition of volume is a well defined one (i.e. any set of orthogonal vectors obtained by the process will give the same volume), and secondly to find a quick way to do this. I managed to prove the first one by induction, but the second part is a little bit of a problem. I managed to obtain formulae for small dimensions as 2,3 or even 4 but this process is impractical for any bigger dimensions as the substitutions for smaller dimensions into the formula for the next dimension becomes exponentially complicated

How does one prove that the gram determinant is equal to the volume of a paralleletope spanned by a set of vectors?

Indirect Proof
Answered

Melina Barber
2022-09-25

$P:.Qv\text{}Q$

Can this be proven without making assumptions for conditional or indirect proofs?

Quadrilaterals
Answered

deiluefniwf
2022-09-25

$angle(A,x,B)=angle(C,x,D)$

Is there a known formula that gives these points ?

Coordinate Geometry
Answered

basaltico00
2022-09-25

Coordinate Geometry
Answered

kennadiceKesezt
2022-09-25

Angle theorems
Answered

madeeha1d8
2022-09-25

We have one main isoceles and another one inside of it. I have attached here a diagram, and we wish to find the angle in red:

The labels blue means : lengths $PQ=QR$ The label green means : lengths $QS=QT$. The given angle $PQS=24$ (deg)

We wish to find angle in red, angle RST.

Geometric Probability
Answered

Darius Miles
2022-09-25

Sir Lancelot and Sir Galahad are doing a shoot out, in which they try to shoot each other while shooting in the same time at each other. The probability of Sir Lancelot to hit Sir Galahad is 0.5 and the probability of Sir Galahad to hit Sir Lancelot is 0.25. All the shots are independent.

A. What is the probability that the shoot out will end in the n's round ?

B. If it is known that after k rounds the shoot out did not end, what is the chance that is will end within two rounds ?

C. What is the chance of Sir Lancelot to win ?

D. What is the chance of Sir Galahad to win ?

Unfortunately, Geometry does not receive sufficient attention from high school students because it is not taught with due explanations. Knowing it well, we provide high school students and parents with high school Geometry questions and answers to make things easier for you as you have to cope with yet another task.

It is not like the list of answers at the end of your textbook because we also have practice answers and various questions answered where you can find the most efficient solutions and see certain rules that make Geometry feel much easier!