# geometric

1. ### What is the geometric mean (representation) of orthogonal matrices?

Could you explain the geometric mean (representation) of orthogonal matrices? The same question is for different types of matrices and also tensors.
2. ### Geometric sequence

How can I find x so that a+x, b+x, c+x is a geometric sequence?
3. ### Help with a geometric proof

Let ABC be a triangle with AC>BC. Let M be the midpoint of the segment AB, D the intersection point of the line AB with the angle bisector of BCA, L the foot of the height through C. Let further E be the touching point of AB and the incircle of the triangle ABC. Let the tangent to the incircle...
4. ### Deriving Ito process with a drift from geometric Brownian motion.

Please help me solve this question. Thank you. Let the Geometric Brownian motion be: âˆ†S/S=Âµâˆ†t + ÏƒÏµsqrt(âˆ†t) âˆ†S = change in stock price (s) Âµ = expected rate of return Ïƒ = volatility of shock Ïµ has standard normal N(0,1) distribution ÏƒÏµsqrt(âˆ†t) = stochastic companion...
5. ### Geometric control theory

What actually the difference between classical control theory and geometric control theory? Are there any problems which cannot be solved by classical theory? Thank you!

Trigonometric Quadrant Suppose that A is a second quadrant angle with sin A = 1/4. Determine the exact value of sin(A/2). The problem has made me crazy. Help please
7. ### Reverse Geometric Series computer program.

Reference : Geometric Progression - Series and Sums - An introduction to solving common geometric series problems. Can we write a Computer program which will print Reverse Geometric number series? Output of the program will be 243,81,27,9,3,1 Can we start from 81 till 1 for the program...
8. ### Geometric progression problem

x(0)=1 x(n+1)=2x(n)+1 S=x(0)+x(1)+...+x(n) S(2018)=? I know that the sequence from x(n+1) is 1,3,7,15,31. Now what do I do? How do I find x(n)?
9. ### Geometric representation of matrix transformation

I want to sketch the 2-vector \textbf{u}=\left( \begin{array}{c} 2\\ 3 \end{array} \right) and its image under the matrix transformation f: R^2\rightarrow R^3 defined by f(u)=\left( \begin{array}{cc} 1 & 0\\ 1 & -1\\ 0 & 1 \end{array} \right)\textbf{u}. Can I sketch both of \textbf{u} and...
10. ### Geometric Probability

Probability with two variables x,y If x\in [0,1] \; and \; y\in [0,1] Find probability such that x+y \leq 1 Question is why we use division of area created by line f(t)=t-1 and total area ? Post solution with explanation
11. ### geometric transformations

Matt wants to reflect a shape over the x-axis and then reflect it over the y-axis. Cathy says that this would be the same as rotating the shape 180 degrees. Do you agree or disagree with Cathy? Justify your answer and use matrix transformations as part of your justification. thanks for any...
12. ### Geometric sequences

https://www.dropbox.com/s/s944t19skpf47d7/1.jpeg?dl=0 Hello everyone, I've attached the question in the link above. I've done part a,b,c but I'm struggling to solve part d. For part d, this is how I tried to solve it: I rearranged the equation from part c: 1/2(a5*b5)=(b6)(a6)...
13. ### Triple Integral of a complex geometric shape

Boundaries: z = 0 z = x + 2y z = 4 - x - 3y z = -y Answer: \int_{0}^{4} \int_{-z}^{4-2z} \int_{z-2y}^{4-z-3y} ~dx~dy~dz = \frac {32}{3} I would be much appreciated if anyone show me the steps of setting the above boundaries...
14. ### Geometric Series Question.

Why is the formula for a geometric series (n+1)a, where the initial term is a, whenever the common ratio is 1? I would have expected it to be a(n) because the upper limit of the summation is n. So it would be a + a + a +... + a, n times. Not n+1 times. Why is it n+1?
15. ### Geometric Series Problem

I have a math problem I cannot solve and don't have access to a teacher! Can someone help me? The sum of three consecutive terms of a geometric sequence is 24 and the sum of the next three terms is also 24. Find the sum of the first 12 terms. It may be super easy and I just haven't...
16. ### Geometric Sequence Question

Someone pls explain how you arrive at this general term. If the common ratio is root2/2 and the first term is 8, I cannot derive the general term. Thanks
17. ### Finite geometric series

I was working on this problem and I was not able to find a starting term to use with the summation formulas for geometric series.
18. ### Geometric experiment

From point C draw two straight lines. ( the angle between them is 1 degree) Between the lines there is arc A. ( radius of arc 100 m) Tangent B appears at the midpoint of A The formulas for calculating A and B do not take into account , the actual radius length ( 100 m or 0.00001 m )...
19. ### Difference between Closed geometric figure & closed set

what could be the difference between a closed set and a closed geometric figure ? Can anyone explain me with an example please.
20. ### Arithmetic and Geometric progression

An arithmetic series has first term -4 and common diffrence of 1.A geometric series has a first term of 8 and a common ratio of 0.5.After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?