Curve Definition and 1000 Threads

We get a "naturally curved" rainbow in nature but while trying to mimic a rainbow in lab, we don't see a curved one... Can't we use the same reason that happens in nature to curve our lab-rainbow

Is not space curvature the curving or projecting into a higher dimension? Like a curved sheet of paper perceived by a two dimensional creature? The mystery seems to reside in our ape brains being unable to perceive (but not conceptualize) higher dimensions than three or relativistic, quantized time.

The volume enclosed by rotating the segment of the curve $y = \frac{1}{2}|x-1|$ between $x = 0$ and $x = 2$ about the $x$-axis is equal to: Is it this simple? Since $x \ge 0$ it's $\frac{\pi}{2} \int_0^2 (\sqrt{(x-1)^2})^2\, dx = \frac{\pi}{3}.$

Hello, I am searching for some kind of transform if it is possible, similar to a Fourier transform, but for an arbitrary function. Sort of an inverse convolution but with a kernel that varies in each point. Or, like I say in the title of this topic a sort of continuous equivalent of fitting a...

Why we sometimes take the area bounded by the curve is sum of positive area and absolute of negative area(e.g. ∫\int_0^2π sin(x)\, dx is equal to 4 or area of ellipse )?But sometimes we just sum positive and negative areas which is equal to 0(e.g. area of cycloid →when we integrate we get...

What is the density of galactic centre? Thus what form of Kepler's law account for the galaxy rotation curve increasing near the galactic centre?

Homework Statement A box shaped vessel, of ##4## compartments and ##80m## lenght, light displacement of ##800## tonnes loads ##200## tonnes in the first compartment and ##200## tonnes in the last compartment. Produce the shearing force diagram and bending moment curve. Homework Equations 3...

I know that the circulation is defined as the counter clock wise integral around the closed curve of the flow velocity component along the curve but what is its meaning in real life? I mean what does circulation actually refer to in real life? Also could someone explain the above image? What is...

I've been struggling with part (a) of this question. I'm not quite sure what the relation is. Any help is greatly appreciated! Thanks! Consider a spiral galaxy with a “flat” rotation curve beyond the central 2 kpc. a. Derive the general relation giving the orbital period, P, of a star (or...

Hi PF/math ! I've been searching for a program which will draw 3d parametric curves accurately for large variables, eg. f(10^8). Ive tried www.math.uri.edu and Ti-Nspire (the latter may or may not have a setting for the accuracy), but both tend to turn what should've been a smooth curve into an...

Homework Statement I have been working on a lab report recently in which I took some data and then further used this data to gather results. I was plotting magnetic flux density as a function of current, this turned out to be an exponential saturation curve. I plotted this curve using a...

Dear, I have a confusion related to the attached image which represents the curve performance of centrifugal pumps. My point is, why is the consumed power, on the same pump curve, is increased as the flow increases?! since the logic for me is the opposite at which the consumed power should...

I've just done an ion chromatography experiment and have normalized my data for a known sample which has a known concentration of 10ppm. I know that the first large peak is due to F- ions and so the area of the peak is propositional to the concentration of the ion. Given that I know the area...

Homework Statement A particle (of mass m) is free to move along a frictionless curve y(x) which is rotating about the y-axis at a constant angular speed ω. A uniform gravitational field (of strength g) acts along the negative y direction. Find the equation of motion of the particle. (That's...

Homework Statement The tangent line of a curve y=e^(-x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin. Homework Equations Ar= xy/2 The Attempt at a Solution Derivative of this function is y'=-e^(-x) I took the formula of the...

i want to calculate area under the curve but i do no not know what function does it satisfies. how should i proceed ?

The program must calculate the length of the curve of ƒ=3.1*x^2-5.3/x between x=1/2 and x=3/2.The legth should be calculated as the sum of n line segments starting with n=1 and ending with n=20. I really can't find why the result I'm getting is wrong.Thanks in advance I am giving you the code...

Homework Statement I am supposed to find the tangent and normal unit vector to r(t)=<2sint,5t,cost>.Homework Equations . The Attempt at a Solution r1(t)=<2cost,5,-sint> which is a tangent vector to the curve, and then to make it a unit vector I would multiply by 1/(sqrt(4cos^2t+25+sin^2t)...

hello. I'm looking for some general guidance as to which methods to use where. i'm wanting to find the force vectors on an object as it moves along a general curve in a space (imagine a roller coaster). for example the parametric curve. z=t x=cos(t) y=sin(t)I know i need to find the partial...

Is there a relatively simple algorithm to compute the area in percentage under the curve as represented by a sigma value? For example; 3 sigma = 99.7 2 sigma = 95 1 sigma = 68.3 Now suppose I wanted to know 2.5 sigma without a table.

I have what I think is a basic question. Say I have a manifold and a metric. How do I write down the most general curve for some arbitrary parameter? For example in \mathbb{R}^2 with the Euclidean metric, I think I should write \gamma(\lambda) = x(\lambda)\hat{x} + y(\lambda)\hat{y} But what...

Two numerical methods for finding the area under a curve are the trapezium rule, where the area is split into trapezia, and the rectangle rule where you split into rectangles. The rectangle rule has two forms, one where you take the height at the midpoint and one where you take the height of the...

Like in the title, is there a software that allows you to draw a curve or even better, input a picture and select a curve on it, in order to get the equation of that curve as a function? Would be glad for help, I need it for my mathematics exploration on minimizing surface area of a vase-like...

then look at : the 2 curves are nearly the same while the equations are not, is there anything wrong ?

Sketch the curve with the given polar equation. θ = −pi/6? I know for certain that its a straight line that passes through the origin but what I'm not sure is if its like this \ or like this /

Hi guys, i have been tasked with matching the upper a theoretical curve (seen in the picture-blue) to the upper experimental part. So far in an attempt to do this i have tried changing a single parameter in the equation i used to generate the theoretical curve, so that the sum of the differences...

The diagram below is from https://en.wikipedia.org/wiki/Galaxy_rotation_curve . I would much appreciate a derivation explaining the shape of the "Expected from visible disk" curve in the diagram. Naively, based on Newtonian mechanics for the orbital velocity of a circular orbit, V = √GM/R ∝...

When Einstein wrote the special realvity he said that inertional acceleration and gravitational acceleration are the same, my question: Does it mean that any source of somthing that making body accelerate (force) is also curving the space-time? for example- spaceship that accelerating in empty...

Homework Statement What is the minimum coefficient of friction needed between the tires and the ground so you make the turn safely?[/B] Car= 1394.7kg You=75kg Radius of turn = 40m Velocity = 20m/s Homework Equations Fnet = MAc (Ac = centripetal Acceleration) = Force of friction Force of...

All though i do not understand all this i wonder what others think, thees extinction seem significantarXiv:1510.01321 [pdf, ps, other] Interstellar Extinction Curve Variations Toward the Inner Milky Way: A Challenge to Observational Cosmology David M. Nataf, Oscar A. Gonzalez, Luca Casagrande...

Homework Statement The parametric equations of a circle, center (1,0) and radius 1, can be expressed as x = 2cos^2(theta), y = 2cos(theta)sin(theta). Evaluate the integral of {(x+y)dx+x^2dy} along the semicircle for which y >=0 from (0,0) to (2,0). Homework Equations Perhaps Green's Theorem...

Homework Statement Given the polar curve r=e^(a*theta), a>0, find the curvature K and determine the limit of K as (a) theta approaches infinity and (b) as a approaches infinity. Homework Equations x=r*cos(theta) y=r*sin(theta) K=|x'y''-y'x''|/[(x')^2 + (y')^2]^(3/2) The Attempt at a Solution...

Hi, 1. Homework Statement C : ℝ→ℝ3 given by C(t)= ( 1/2 [ (1+k)/(1-k) cos((1-k)t) - (1-k)/(1+k) cos((1+k)t) ] ; 1/2 [ (1+k)/(1-k) sin((1-k)t) - (1-k)/(1+k) sin((1+k)t) ] ) with 0<|k|<1 Show that C(t) is an epitrocoid and find R, r and d according to k Homework Equations Parametrization of...

Hello ! Homework Statement Consider a parametrized curve C(θ)=( (R+r)*cos(θ) - d*cos(θ(R+r)/r) ; (R+r)*sin(θ) - d*sin(θ(R+r)/r) ) Show that C is regular for d<r. Is it regular if d=r ? Homework EquationsThe Attempt at a Solution C'(θ)=( -(R+r)*sin(θ) +d*(R+r)/r*sin(θ(R+r)/r) ; (R+r)*cos(θ) -...

Homework Statement y^2 + 3x - x^3 = C, C\in\mathbb{R}\setminus\{0\} Homework EquationsThe Attempt at a Solution Keeping in mind that ##\cos ^2\alpha + \sin ^2\alpha = 1## I would go about it \left (\frac{y}{\sqrt{C}}\right )^2 + \left (\frac{\sqrt{3x-x^3}}{\sqrt{C}}\right )^2 = 1 would then...

I am doing an experiment that generates data in three 1-hour-blocks. Each block has a different number and timing for acquisitions. (The first hour is more frequent and numerous, while the last hour is only 6 acquisitions) The reason for breaking it up into 3 hours is to give the subjects a...

Well, it's physics friday! (carpe diem etc, what else) :) 1. Homework Statement I present to you this (not so) pleasant expression that seemingly appeared on a page out of nowhere. \vec{F}(r, \theta, \varphi) = \frac{F_0}{ar \sin\theta}[(a^2 + ar \sin\theta \cos\varphi)(\sin\theta \hat{r} +...

Suppose you have a given area under a curve, say 250, and want to come up with a function that produces this value. How would you do this? Although I came up with two basic functions as follows:First: Let y (x) = 5 from 0<x<50 , thus length*width = yx = 5*50 = 250. Second: Area of a...

Homework Statement The figure shows the stress-strain curve for a material. The scale of the stress axis is set by s = 280, in units of 10^6 N/m2. What are (a) the Young's modulus and (b) the approximate yield strength for this material? Homework Equations E=stress/strain The Attempt at a...

Δ≤ Homework Statement Find final velocity. Knowns: m = 4kg Initial v = 0 m/s F = Asin(xt) F = (2000N)(sin(\frac{1000π}{sec}*t) (0sec ≤ x ≤ .001sec) We need to find the impulse from a Force vs. Time graph. There is a preface to this problem that says if we work out the Force function...

I plotted a graph on Origin software and need to do curve fitting to get accurate results. From my understanding, I need to provide a function for the fitting. So how do I derive the function? I am actually provided with the function I(x)=I0-I1cos(x-x0) and this function will fit the lowest...

Hey, I'm only asking this here because its a bit of a time-critical question (no pun inteded). But if one takes a V Vs I curve (like to measure BH without the equipment to measure flux directly), that is to say, measures the change of increase in voltage and increase in current (where current is...

This isn't a precise homework question, but this seemed like the most reasonable place to post. If not, please feel free to move it. I have a large set of data points that should fit to a known equation (the Drude-Smith model for conductivity) The equation the data should fit to is: σ(ω) =...

Homework Statement A car traveling 10 m/s is moving along a track banked at 5 degrees. The tire-road friction coefficient is .3 What is the minimum radius it can travel without slipping? v0= 10 m/s Bank Angle Θ = 5° μ=0.3 Note I am working through prep material for the exam. The solution...

Hi everyone, Thanks for visiting my post. I was wondering if you guys know what kind of software I must use to draw complicated curves. I already have the equations. For example, for lemniscate I would use following: 2(x^2+y^2)=25(x^2-y^2) I appreciate the help.

I am programming a game in which there are no outside forces acting on the car aside from the engine. I will not be having gears, so that is not a factor. I just want to know if there is an equation I can use to calculate the car's speed at any given time. The car will start off accelerating...

Hi everyone, I have an exercise I haven't solved yet, please help me. Find the length of the curve: $$y = \frac{{x}^{5}}{6} - \frac{lnx}{4}, 2 \le x \le 4$$.

Homework Statement Hi all, I'm trying to calculate a parameter of polymers known as the fragility index. I've attached an image of this curve, which can be either strong of fragile depending on the material. The image also contains the definition for calculating this. However, I don't...

Homework Statement [/B] Show that the given parametric curve decribed by the following notations: x=cos(t), y=sin(t), z=2+2cos(t) lies in a single plane ,find the normal vector to this plane Homework Equations --- [/B] r(t)=cos(t) i + sin(t) j + 2+2cos(t) k The Attempt at a Solution My...

Rather a short question, but what kind of design can be used for a narrow potential surface curvature in molecules?