Geometry Definition and 999 Threads

I find it interesting that so many know how to use all kinds of apps on their cell phones, but so few are able to do simple algebra any more. If you ask around, engineers not included, I think you would find very few people e.g. to be able to find the axis of symmetry of the parabola ##...

(a) The hint from question is to used geometrical argument. From the graph, I can see ##r_1+r_2=c_2-c_1## but I doubt it will be usefule since the limit is ##\frac{r_2}{r_1} \rightarrow 1##, not in term of ##c##. I also tried to calculate the limit directly (not using geometrical argument at...

Gave following to bing chat and chatgpt, Both gave wrong answers. Any thoughts? ------------------------------ Geometry problem: Semi-circle inside triangle: Triangle with known length sides a, b, c where a is the longest. Place inside the triangle a semi-circle with entire diameter resting...

Can anyone explain the meaning behind a mobius strip? Basically just a means to travel on both sides of a flat surface? It's still a 3D object though since it uses 3D space for the twist to be possible?

Can AI or GPT-4 answer the following? ------------------------------- Geometry problem: Triangle with known length sides a, b, c where a is the longest. Place inside the triangle a semi-circle with diameter on side a. What is radius of largest possible semi-circle in terms of side lengths?

This is an Argand diagram showing the first 40,000 terms of the series form of the Riemann Zeta function, for the argument ##\sigma + i t = 1/2 + 62854.13 \thinspace i## The blue lines are the first 100 (or so) terms, and the rest of the terms are in red. The plot shows a kind of approximate...

I suppose there is a database for that, but I can't find it. Could anyone send here a link?

In the figure, the point S is located inside the section FE. Starting from S, as indicated in the figure, six circular arcs are drawn step by step around arcs around A, C, B, A, C, B are drawn. Show that the sixth arc leads back to S and that the six arcs together are then exactly as long as the...

Hey Condition 1: A 2D infinite plane and there is a circular hole in the middle. When t=0, an impulsive loading, P=f(t), is applied to the boundary of the circle(outward), so the wave will start at the boundary of the circle and propagate in the plane Condition 2: A 3D infinite plane and there...

What geometry theorem is used to be able to state that 8/4 = x/6 ??

So I've got the following problem: I have points A, B, and C which form a triangle in a 3D space (each point of the triangle has x,y, and z coordinates). I need to find out on which side of the triangle point D lies. I do not have access to the normal of the triangle. How am I supposed to...

TL;DR Summary: Looking for books similar to "The Wonder Book of Geometry" by David Acheson I loved David Acheson's "The Wonder Book of Geometry". Can you recommend other books like that?

Hi, I'm differentiating the "z" function to find extreme points but after solving the first partial derivatives with respect to "x" and "y" and also the "x" variable of the system, I can't find "y" (still in the system) using "ln" (natural logarithm). The question is can I differentiate both...

This is the textbook question. I do not have the solution. I am pretty stuck on this one:cry: My attempt on this...find my rough sketch here; From my analysis; ##x+x+m+m=180^0## angles opposite each other on a cyclic quadrilateral... I have point ##O## as the centre of the circle...

Text question is here and solution; My approach; ##BP ×AP= PT^2## Let ##AP= x## Therefore, ##(6+x)x=16## ##x^2+6x-16=0## ##x=2## or##x=-8## ##⇒x=2## positive value only. I guess this may be the only approach. Cheers!

I’m teaching myself algebra right now so I’m not at that point, but I was wondering when I finish algebra what should I study next? Trig or Geometry?

As I understand it, the flatness problem of Bob Dicke, says a flat universe in unstable and so has to be set very precisely in the early universe to give us the flat universe we see today. Is this the same problem as saying the expansion rate had to be finely tuned and if so how are the two...

Fun with tiled cyclic quadrilaterals

I saw 2 recent papers on MOND are they promising [Submitted on 21 Jul 2022] Noncommutative geometry and MOND Peter K.F. Kuhfittig Comments: 5 pages, no figures Subjects...

Schwarzschild Geometry-proper distance. From what I have studied when the Schwarzschild line element is evaluated at constant time and at a constant radius , proper distance becomes a Euclidean distance on the surface of a sphere. What I don't understand is how to evaluate the integral...

I have some questions about the space of the rectangle shown in the spacetime diagram. The red and blue lines are world lines of objects at rest with each other. 1) Does the rectangle have an area? (if no please go to question 3) 2) Is the rectangle a 2d Euclidean space? (if no please go to...

Hey,... is that correct to say that "The null part added to itself will always remain the same as itself, namely null."" In arithmetic, 3 * 0 = 0 + 0 + 0 = 0; It is therefore healthy to extrapolate as follows:∞-1 * 0 = 0 + 0 + 0 +... + 0 + 0 + 0 + 0 = 0 ∞ * 0 = 0 + 0 + 0 +... + 0 + 0 + 0...

Hello all. I'm an undergraduate student looking to conduct an experiment with an isotope that undergoes beta decay. I am curious as to the degree to which the isotope geometry will reduce the energy of/deflect beta particles emitted from the isotope. By geometry, I mean the "shape" of the...

(a) Let be m a line and the only two semiplans determined by m. (i) Show that: If are points that do not belong to such , so and are in opposite sides of m. (ii) In the same conditions of the last item, show: and . (iii) Determine the union result , carefully justifying your answer...

Dear all, I am writing a vehicle dynamics simulation for my thesis topic. However, I came into a conundrum when testing the cornering behavior of my vehicle. The problem is inherently complex due to its many subsystems, but I'll try to give as much detail without bogging the thread down...

Dear all, the following problem is not a home-work problem. I have come up with this question for myself. Nevertheless, I am stuck and need your help. The question is: Can I calculate the distance between points A and B from this information? And if yes, how? I think it should be possible...

https://www.quantamagazine.org/father-son-team-solves-geometry-problem-with-infinite-folds-20220404/

Consider the following example: Point A has coordinates 45 lat, 0 long. Point B has coordinates 45 lat, 2 long. Both points are 5000 ft above sea level. The distance between them is X. Point C has coordinates 45 lat, 100 long. Point D has coordinates 45 lat, 102 long. Both points are at sea...

I want to use this to design a parabolic (optical) mirror; The problem is that in my application I need both D and f to be a parameter, but I need to specify f only as a perpendicular distance from D. In other words, I need to specify some f_2=f-d, and calculate d. I can't seem to come up with...

Trying to calculate a circumference of a sphere from a radius of 3.09 inches. Is 19.4 a correct answer? Just ran numbers in the first circumference calculator I found http://calcurator.org/circumference-calculator/. Can I use the same formula for a sphere? What can I say ...Geometry is not my...

Hello everyone, I wanted some help deciding which elective to choose. I am a junior and for my next semester I have the option to pick either Differential Geometry-I or Quantum Information. I am confused which one to choose. We will be doing QMII as a compulsory course next semester and I have...

Hi, I'm wondering why shorted circuit geometry like figure 2 did not sense photocurrent? Even if the the circuit composed like 2, I guess that by the Kirchhoff's Law, voltage should apply to the ampere meter and photocurrent should be sensed. But in real experiment, I found that shorted circuit...

Are there any major difference between the first and second edition of Geometry, by David Brannan. Besides price of course.

Problem: Given the line L: x = (-3, 1) + t(1,-2) find all x on L that lie 2 units from (-3, 1). I know the answer is (3 ± 2 / √5, -1 ± 4/√5) but I don't know where to start. I found that if t=2, x= (-5, 5) and the normal vector is (2, 1) but I am not sure if this information is useful or how...

I'm reading about excitation of surface plasmons, and there's a claim in the derivation I don't know how to prove. The geometry is two infinite slabs of material with negligible permeability (##\mu_1 = \mu_2 = 1##) and different permittivity ##(\epsilon_1 \neq \epsilon_2 \neq 1)##. The claim...

This is a textbook problem...clearly angle ##AEG≠ 160^0## there is something wrong with the value given,...I am trying to analyse this...

Hello, so I saw this problem on a website while looking up trigonometric identities and trying to solve it. what I know: The internal angles add up to pi Let the tangent point between A and B be X Let the tangent point between B and C be Y Let the tangent point between C and A be Z ##...

I have calculated the height of the segment using the Pythagorean Theorem and that's currently where I am right now. I don't seem to find any equations that can help me. Though I might be not trying hard enough or using the wrong words because I'm not really fluent in mathematical terms as you...

This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that there is an constat vector 'a' that satisfy a•r=constant, than the motion would be on the surface of a cone. So i tried to make...

Pictured below are two hinged panels that can rotate upward to form an upside-down V. In position 1, the panels are lying flat. In position 2, the panels have folded together and the joined edge is raised up. Normally, in order to actuate this hinging motion, one would need to manually lift the...

Saw this on "Who Wants to Be a Millionaire" which, of course, I'd never trust on its own, so I verified: It is common practice to cut flower stems at an angle, but I never thought to confirm why. I assumed it had something to do with cutting across the grain like one does with meat...

Hello folks, I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct...

Dear Everyone, So I would like some recommendation for high school geometry books that are affordable and preferably e-books. Why do I need some books on high school geometry? I would like to improve my geometric reasoning. When I took high school geometry a decade and half ago, I was...

I was just browsing through the textbooks forum a few days ago when I came across a post on differential geometry books. Among the others these two books by the same author seem to be the most widely recommended: Elementary Differential Geometry (Barret O' Neill) Semi-Riemannian Geometry with...

Computing timelike geodesics in the Schwarzschild geometry is pretty straightforward using conserved quantities. You can treat the problem as a variational problem with an effective Lagrangian of ##\mathcal{L} = \frac{1}{2} (Q \frac{dt}{d\tau}^2 - \frac{1}{Q} \frac{dr}{d\tau}^2 - r^2...

I'm imagining something like this: The image was taken from the following paper, and is described as a rhombicuboctahedral quasicrystal. The paper itself gets very technical (at least for me), describing projecting a 4D crystal into 3D space. It seems to me based off of a rhombicuboctahedron...

I am looking for math books that focus on geometrical interpretations. Sadly most of the modern books lack these interpretations and only consists out of theorems and proofs. It seems to me that most modern mathematicians are pure left-brain sequential thinkers that do not have a lot of...

I am in the middle of a problem for the Kerr geometry, I need to do the integral ##\int_{\mathcal{N}} \star J## over a null hypersurface ##\mathcal{N}## which is a subset of ##\mathcal{H}^+##, where ##J_a = -T_{ab} k^b## and the orientation on ##\mathcal{N}## is ##dv \wedge d\theta \wedge...

Can anyone recommend a good on-line class for differential geometry? I'd like to start studying GR but want a good background in differential geometry before doing so. Many thanks.