## Arc-length-parametric-equations

From Omilili

### Circle center and angle with points on the circle

I recommend reading http://www.ajdesigner.com/phpcircle/circle_arc_length_theta.php It has all the equation and even a handy calculator Regards PS: It took me a couple minutes to google FYI Hi, did the link Serguey123 fit your needs? If not: you could calculate the CenterPoint of the circle

### Finding arclength.. using simpsons rule ..helpp??

Use Simpson's rule with n=10 to estimate the arclength of the curve. y= x ln x , 1<x<3 So length equation, (integral from 1to 3) sqrt[1+(1+lnx)^2] dx... this is where I am stuck at, how would Use Simpson's rule with n=10 to estimate the arc length of the curve. y= x ln x , 1<x<3 So I started to find the derivative...

### Length of arc?

To get AC to measure the length of this arc. either with spline or polyline. I'm sure I missing together but each point I click resets length to zero again. And bending straight line so far gives from the left. Peter Devlin I found on the web an equation for arclength that does not involve trig

### Curve parametrized by arclength

Let A:I-->R^2 be a curve parametrized by arc length.Then A is a segment of a straight line ..Can you Help me?any start.. if s is arclength..then A is parametrized by arclength, means... Quote: : Let A:I-->R^2 be a curve parametrized by arc length.Then A is a segment of a straight

Question:http://s676.photobucket.com/albums/vv124/rockine1993/?action=view¤t=geom_365bb.jpg http://s676.photobucket.com/albums/vv124/rockine1993/?action=view¤t=geom_365c.jpg http://s676.photobucket.com/albums/vv124/rockine1993/?action=view¤t=geom_365a.jpg 31: At five o'clock the measure of the angle formed by the hands of the clock is? 60 210 150 180 32: In angle ABC, A is the vertex. True False Neither Both 33: A regular polyhedron is a polyhedron with faces that are congruent squares. True False Neither Both 34: In Figure 7 if m Arc PM = 40 and m Arc JKM = 210 , then m Ang PJK = 70 35 55 40 35: If a triangle has sides of lengths 8, 4, and 4 sqrt(3), is the triangle right? Yes No Maybe Sometimes 36: A triangle with at least two sides of equal length is called _______. Scalene Isosceles Equilateral Regular 37: A polygon is regular if and only if the sides are congruent ( if and only if states a condition but does not necessitate it to be the sole condition). False True Neither Both 38: In the proof above, the reason for step 5 is substitution parallel postulate equal corresponding angles angle addition 39: What is the center of the circle with equation (x + 1)^2 + (y + 3)^2 = 9/4? (-1, -3) (-1, -1) (-3/2, 4) (1, 3) 40: Use Figure 2 above. If m Ang B = 53 and m Ang C = 62 , which side(s) of Triangle ABC is(are) the longest? AB BC AC AB & BC 41: What is the equation of the line with slope 2/3 and passes through the midpoint of the segment joining points (-1, 6) and (-7, -4)? y = -3x - 9 y = (2/3)x + (11/3) y = -3x - 7 y = (2/3)x - 6 42: In the proof above, the reason for step 4 is substitution angle addition equal corresponding angles parallel postulate 43: For Figure 4, find DE. 6 8 10 12 44: If two triangles are congruent, then the _______ corresponding parts are congruent. 3 6 4 2 45: Lines p and q are parallel. The slope of p is 5 and the slope of q is 10/v. What is v? 2 sqrt(13) 4 4 sqrt(2) 2 46: For Figure 6, 0A = 3 and AC = 12, what is OB? 3sqrt(9) 3 sqrt(3) 7 sqrt(153) 47: Classify the angle with measure 75 degrees. Acute Obtuse Straight Right 48: A parallelogram of area 78 square units has one side of length 12. Find the length of an altitude to that side. 3 2 sqrt(3) 6 6.5 49: Refer to Triangle DFE in Figure 5, if DM = 4 and ME = 8, what is FM in simplified form? 4 sqrt(2) 12 2 sqrt(3) 16 50: In elliptic or spherical geometry, there can be _____ right angle(s) in a triangle. zero one two three 51: For right triangle ACB with right angle C, if m Ang A = 45 and BC = 3, what is the length of AC? 3 sqrt(3) 3 3 sqrt(2) 1.5 52: Opposites sides of a parallelogram are parallel and congruent. True False Neither Both 53: In the proof above, the reason for step 3 is substitution angle addition parallel postulate equal corresponding angles

Question:As a follow-on to http://answers.yahoo.com/question/index?qid=20080404190545AAwI6UO and referring to this diagram: http://nrich.maths.org/askedNRICH/edited/2360.html (but using my notation, not his) I want to talk about the general eqn for line PQ, NOT just shortest distance itself. Two questions: 1) Critique my working and suggest any improvements. 2) We end up with three eqns in two parametric variables (s,t). How can we be sure that this overdetermined system has any solution in s,t? Given any two skew (non-intersecting) lines: Line LP : x = a + sb Line LQ : x = c + td >Hint: the line joining P and Q is perpendicular to both lines PQ must be parallel to (a b), so form the unit vector in that direction: n = (a b) / ||a b|| Now take any (non-shortest) vector which is known to go between lines LP and LQ, such as (c-a), and project it onto n: a + sb ||(c -a) . n|| n = c + td (a-c) ||(a-c) . n|| n = (td -sb) => Three eqns in two variables s,t I think the missing third variable is r, an arbitrary-length vector in the direction of n. => Three eqns in three variables Or something like that. Please help tie up this loose end and rewrite: (a-c) ||(a-c) . n|| n = (td -sb) scythian - thanks. It simplifies a bit if we write (a-c) =u in: e = (a-c) +Sb -Td = u +Sb -Td Can you simplify your result algebraically? It looks like a determinant, or two separate determinants to me?

Answers:Let me try my hand in this. Let a, b, c, d be vectors in 3D space, and S, T be scalar variables, so that we have two skew lines a+Sb, c+Td. The difference, e = (a+Sb) - (c+Td), is a vector connecting the two lines, so that the shortest such vector would have the property e . b = e . d = 0. If we expand both, and solve the simultaneous equations, we end up with the following scalar quantities S, T: S = ((cd - ad) bd + (ab - cb) dd) / ((bd) - bb dd) T = ((ab - cb) bd + (cd - ad) bb) / ((bd) - bb dd) where ab, ad, cb, cd, bd, bb, dd are all vector dot products. Incidentally, the same result can be found by finding minimum S & T through partial differentiation of the vector length of e. Addendum: Well, let's see, if a - c = u, we can rewrite the equations as: S = (ub dd - ud bd) / ((bd) - bb dd) T = (ub bd - ud bb) / ((bd) - bb dd) The form does vaguely remind me of terms found in differential geometry, as for example EG - F , which is a determinant of the first fundamental form.

### Trig: The Unit Circle, Degrees & Radians

www.mindbites.com This 80 minute trigonometry lesson is a study of the Unit Circle (a circle with a radius of one unit) and its x and y coordinates. This lesson will show you how to find the exact value of the six trig ratios of: - all quadrantal angles 0 or 2 Pi radians, Pi/2 radians, Pi radians, 3Pi/2 radians, - angles with a reference angle of Pi/4 radians (45 degrees) - angles with a reference angle of Pi/6 (30 degrees) - angles with a reference angle of Pi/3 (30 degrees) Thislesson contains explanations of the concepts and 12 example questions with step by step solutions plus 5 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson include: - 300 Basic Trigonometry Part I (www.mindbites.com - 315 Basic Trigonometry Part II (www.mindbites.com - 320 Trigonometry on the Coordinate Plane (www.mindbites.com - 330 Arc Length Solving 1st Degree Trig Equations (Radians) (www.mindbites.com

### Character TD reel

-------- 00:02 - 00:06 project: Beware the Snake 3D Software: 3Ds Max Short movie. It was realized completely by myself, from the concept to the final compositing. -------- 00:07 - 00:31 project: EP_spine 3D Software: Maya Personal project. A quaternion spine rig, based on a C++ DG node, and related MEL scripts. Features: - Custom shape for vertebras. - variable number of vertebras. - variable deegre of the curve. - variable number of CTRLs to define the shape of the curve. - ramp control for distribution of the spin along the curve. - ramp control for distribution of the squash. - ramp control for distribution of the stretch. - parametric length factor or arc length factor defining the position of each vertebras along the curve. A single node is connected to every vertebra transform. This was done for having a fast real-time computation. -------- 00:32 - 00:53 project: Sym_Map tools + EP_relax 3D Software: Maya Personal project. 1) Sym_map: C++ node, custom commands (C++), and related MEL scripts to provide a way to symmetrize any type of weightmap (blendshape, deformers, etc..): it stores the informations about symmetric vertices in a sym_map node, than apply the symmetrize commands retriving vertex relationships looking trough this node, regardless of the actual mesh shape. 2) EP_relax. C++ deformer used to get rid of unproper deformations. It is a combination of two separated effects: a relax one and a push one. Each of these two effects is provided of its own ...

### Calculus: Inverse Sine, Cosine, and Tangent

Watch Full lesson here: www.mindbites.com This lesson is part of a series: Calculus In this lesson, you will learn about the existence of trigonometric inverse functions when the domain is restricted. Though trig functions are not one-to-one, they do have defined inverses. Professor Burger will walk you through an explanation of how you arrive at the inverse sine, inverse cosine, and inverse tangent functions. Inverse trig functions can be denoted by inverse notation or with arc-notation, and his lesson will cover both of these methods of notation. This video should serve as in introduction to arcsin, arccos, and arctan functions. Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at www.thinkwell.com The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'H pital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

### Top Ten Theorems: Metric Geometry Part 3

Theorems #4, #3, #2, #1 count down completed. Contraction of a rank two tensor to an invariant scalar. Derivation of the General Relativistic field equations for empty space. The arc length integral in n-dimensions. Properties of a diagonal metric tensor. Covariant and contravariant unit vectors, and the ortho-normal basis set.

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