Geometry Definition and 999 Threads

Is known that in every rectangle triangle the following relationships are true: But, how use geometrically the function sinh, cosh, and tanh?

Given two segments of lengths $x$ and $y$, construct with a straightedge and a compass a segment of length $\sqrt[4]{x^4+y^4}$.

In all the literature that I have seen it is mentioned that these two are "branches" of integral geometry, but no where I can see the exact connection since one is connected with probability and the other is an integral. I have seen this, but it is not clear...

Hello, i'm struggling to understand the equation I've been given for finding the radius of a sphere by using a spherometer. I wasn't sure if this would be better in the physics section, but I figured it is essentially geometry. Homework Statement "From the diagram, simple geometry...

Homework Statement So I'm doing a physics problem, and I think I'd get the right answer if I solved this triangle. I don't know any angles. The base is 56 meters long, its height is 500 meters, and the difference between the other two sides is 4 meters. Can I figure out the sides based on this...

Do you know how could I interpret the Einstein Tensor geometrically (on a general manifold)? For example the Christoffel Symbols can show someone the divergence/convergence of geodesics and/or show how the change of metric from point to point creates an additional force/potential (through the...

I am always entranced when I read in calculus books about various curves like lemniscates, cardioids, the spiral of Archimedes, the witch of Agnesi, and similar things. But in calculus books they are generally just little asides or relegated to the exercises. Presumably there is more to analytic...

I've been thinking about the geometry of spacetime itself, and it has really been mind-blowing in some way. If space and time are so alike that we can treat them in a way that objects have a temporal extension as well as a spatial one, my question will be about this fact. So let's suppose...

In physics, when we draw a block on an incline, we know that the angles are the same see image: Incline angle = angle formed by Mg, M, F_2 I can't recall what geometry properties allows us to make this statement.

It is basically a question in computer graphics but I guess math sub-forum will suit this question. While rotating a point, why we first apply yaw, then pitch and then roll in that order? Of course if we change the order, final rotation changes but why this specific order works? Some proof or...

(BMO, 2013) The angles $A$, $B$, $C$ of a triangle are measures in degrees, and the lengths of the opposite sides are $a$,$b$,$c$ respectively. Prove: \[ 60^\circ \leq \frac{aA + bB + cC}{a + b + c} < 90^\circ. \] Edit: Update to include the degree symbol for clarification. Thanks, anemone.

What are great compass, protractor and ruler brands for geometry? I want to learn geometry properly and I need to invest in some tools. Price is not an issue if the tools will last many years

I am Looking for some books about Differential Geometry,and I just begin to learn Differential Geometry,so who can introduce some books about Differential Geometry that suitable for Beginners to me,and tell me where can download the PDF document of the book. thanks

I have been teaching myself QFT and General Relativity. The mathematics of those fields is daunting, and I find that what I have come across is very difficult to master. Of course it will take work, but can someone recommend a good text for self-leaning differential geometry with application...

How to create a script geometry. Is it possible? some type? I need to create a script to pipe conveyor. After entering the input data is created geometry. pls help me

I am really not sure where to even start with this question, at which point, (A,B,C) would the dog have a maximum area to play if tethered by a 20ft leash?

I have attached the geometry of interest with some parts of the solution. The geometry is a vessel that is half of a sphere with an orifice at the bottom. The first expression that they have written, the "A*(2*g*z)^0.5=..." is from conservation of flow rate. 2*g*z is the velocity at the...

Just for clarity, the geometry of the universe is completely determined by the stuff that the universe contains. The parameter k in the R-W metric and in the Friedmann equation *is determined* by the density. The curvature/ geometry of the universe is not independent of the density. Correct or...

Geometry -- Help with theorem proof please Homework Statement Let ##A,B,C,D## be points. If ##\vec{AB} = \vec{CD}## then ##A=C##. Homework Equations None The Attempt at a Solution This question was a theorem in my book that wasn't proved. I am wondering how to prove it? It is saying...

Hello, I am learning General Relativity through some books like 'Gravity' by Hartle and through some other textbooks. All those books, do not speak of general relativity from the context of differential geometry. I have a fair amount of knowledge of calculus as well as set theory. My...

Hello I've got a problem with Cartesian Geometry and cannot find a solution. A will appretiate any help I can get. b) Show that $$[AQ]$$ has equation $$cx + by = -2ac$$ c) Prove that the third median $$[BR]$$ passes through the point of intersection $$G$$ of medians $$[OP]$$ and $$[AQ]$$...

Homework Statement Prove that a line in a metric geometry has infinitely many points.2. The attempt at a solution I can't use any real analysis, like completeness. I can only use geometry to prove this, specifically distances and rulers. Intituvely I understand why. Any segment with at least...

Hello PF! After months of eye shopping, I couldn't help but join this awesome community myself. I am a high school senior entering college soon, who is very excited to take college-level physics! I've done some research of what classes I should take, and came upon a conflict of scheduling...

Homework Statement Show that for any trajectory r(t) the acceleration can be written as: \mathbf{a}(t)=\frac{dv}{dt}\hat{T}(t)+\frac{v^2}{\rho}\hat{N}(t) where v is the speed, T is a unit vector tangential to r and N is a unit vector perpendicular to T, at time t. rho is the radius of...

Homework Statement Let ##\mathbb{R}^2 = \{Q = (a,b) | a,b\in \mathbb{R}\}##. Prove that if ##q_1 = (a_1,b_1)## and ##q_2=(a_2,b_2)## are equivalent, meaning ##a_1^2+b_1^2 = a_2^2 +b_2^2##, then this gives an equivalence relation on ##\mathbb{R}^2##. What is ##[(1,0)]...

I'm getting interested in mathematics because as a philosopher I am upset with the amazingly poor standards of rigor in my field. I am looking to mathematics for guidance. I would like to formalize philosophy and turn it into a deductive science. I have a deep interest in logic so I decided...

refer to the following image so consider the angle of the yellow theta on the top left. this is 45*. if we fix one side of both red lines at the blue circles, and we slide the other end along the green side of the cube, ie just think of the green lines as rails for the red lines to slide...

I am a 3rd year mechanical engineering student at LSU, but my true interest lies in theoretical physics and mathematics (specifically general relativity and differential geometry). I've taken calculus 1,2,3, linear algebra, ordinary differential equations, number theory, discrete math, and...

Hello, This thread is about the two books by Naber: https://www.amazon.com/dp/1461426820/?tag=pfamazon01-20 https://www.amazon.com/dp/0387989471/?tag=pfamazon01-20 The topics in this book seem excellent. They are standard mathematical topics such as homotopy, homology, bundles...

Think for example of the torus as a square with the proper edges identified. Viewed like this (i.e. using the flat metric), it clearly has zero curvature everywhere. More specifically, it seems Euclid's axioms are satisfied. But however we have non-trivial topology. So what's up? Or is...

Hi, Please refer to the Pythagorean proof of the theorem that the angels in a triangle add to 180 degrees. The following link has the proof. http://www.cut-the-knot.org/triangle/pythpar/AnglesInTriangle.shtml You will note that this proof is based on the assumptions that angles on a straight...

Hey guys, I was looking at both the time-dependent and time-independent schrodinger equations, and I notice that we often choose to solve these in spherical coordinates. I understand that we do this because they are convenient for problems with azimuthal symmetry. However, how do we know that...

Vector algebra and analytical geometry textbook I have a very comprehensive textbook written in portuguese about vector algebra and analytical geometry, but the author didn't include a bibliography at the book's end. What textbooks, in english, contains these syllabus (I'm pasting the list of...

hey pf! so my question is how cramer's rule makes sense from a geometric perspective. I'm reading the following article: http://www.maa.org/sites/default/files/268994245608.pdf and i am good with the logic of the entire article except one point: when they say $$x=\frac{ON}{OQ}$$ can someone...

Should I start with Euclid geometry?? Iam doing electrical engineering course(undergrad first year). I like to see how mathematics works in it's core. From grade 6(when I was 11), when I was introduced algebra, I did my maximum to know how things worked..I would want to know how a particular...

Homework Statement In Rectangle ABCD, AB=4 and BC=3. Find the side length of Rhombus AXYZ, where X is on AB, Y is on BC and Z is on BD. 2. Relevant Questions: The Attempt at a Solution Hi, so here's my picture for the problem...I tried to draw the exact picture with exact value...

I'm taking a class on Geometry next semester an I'm in need of a good book. It will be both euclidean and non-euclidean geometry and is a proof based course. Sorry, I know that's rather vague but that's all I know about the class. Thank you!

Hi, I was wondering if someone know of a solution book for this book, I'm studying for final, having lot of problem with this class... (not my type of math I guess!) Thanks

Problem: The median AD of the $\Delta$ ABC is bisected at E. BE meets AC in F. Find AF:AC. Attempt: Let point E divide BF in the ratio $\mu : 1$ and let F divide the line AC in the ratio $\lambda : 1$. I take A as the origin. Then, $$\vec{AD}=\frac{1}{2}(\vec{AB}+\vec{AC})$$...

Hi. I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic geometry in my spare time and had a simple question about the topic. If a straight line in Euclidean geometry is a hyperbola in the hyperbolic plane (do I have that right?)...

Here are the questions: I have posted a link there to this thread so the OP can see my work.

I'm a physics major interested in taking some upper level math classes such as topology, differential geometry, and group theory but these classes are only taught in the math department and are heavy on the proofs. Analysis are recommended and preferred prerequisites but are apparently not...

Homework Statement Using the curve \vec{a}(u,v)= (u,v,uv) for all (u,v) ε R^2 Find the matrix for d\vec{N} in the basis of {\vec{a}_{u},\vec{a}_{v}} Homework Equations Well first off i found the partial derivatives \vec{a}_{u} which is 1,0,v, while \vec{a}_{v} is 0,1,u Then using those...

Consider a 2-sphere on the real plane equipped with the linear map from the sphere to it's equatorial 2-plane by fixing the topmost vertex of the sphere. This is now an analogue of the Riemann sphere in 3-dimensional space, hence we have the "point at infinity" in addition to the usual reals...

hey pf! i am studying fluid mechanics and was wondering if any of you are familiar with a flow around some geometry? for example, perhaps a 2-D fluid flowing around a circle? if so please reply, as i am wondering how to model the navier-stokes equations. i'll be happy to post the equations...

Has anyone considered whether particle entanglement might involve an extra-dimensional substructure of spacetime which negates the need for superluminal communication between entangled particles? If so, what characteristics would such a geometry need to instantly connect particles? Or is it...

I am reading Dummit and Foote: Section 15.2 Radicals and Affine Varieties. On page 678, Proposition 16 reads as follows: (see attachment, page 678) --------------------------------------------------------------------------------------- Proposition 16. Suppose \phi \ : \ V...

I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a morphism or polynomial map of algebraic sets as follows: ---------------------------------------------------------------------------------------------- Definition. A map...

Dummit and Foote Section 15.1, Exercise 24 reads as follows: --------------------------------------------------------------------------------------------------------- Let V = \mathcal{Z} (xy - z) \subseteq \mathbb{A}^3 . Prove that V is isomorphic to \mathbb{A}^2 and provide an explicit...

Dummit and Foote Section 15.1, Exercise 24 reads as follows: --------------------------------------------------------------------------------------------------------- Let V = \mathcal{Z} (xy - z) \subseteq \mathbb{A}^3 . Prove that $$ V $$ is isomorphic to \mathbb{A}^2 and provide an...