What is Normal: Definition and 1000 Discussions

In geometry, a normal is an object such as a line, ray, or vector that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the (infinite) line perpendicular to the tangent line to the curve at the point.
A normal vector may have length one (a unit vector) or its length may represent the curvature of the object (a curvature vector); its algebraic sign may indicate sides (interior or exterior).
In three dimensions, a surface normal, or simply normal, to a surface at point P is a vector perpendicular to the tangent plane of the surface at P. The word "normal" is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality (right angles).
The concept has been generalized to differentiable manifolds of arbitrary dimension embedded in a Euclidean space. The normal vector space or normal space of a manifold at point P is the set of vectors which are orthogonal to the tangent space at P.
Normal vectors are of special interest in the case of smooth curves and smooth surfaces.
The normal is often used in 3D computer graphics (notice the singular, as only one normal will be defined) to determine a surface's orientation toward a light source for flat shading, or the orientation of each of the surface's corners (vertices) to mimic a curved surface with Phong shading.

View More On Wikipedia.org
Recent contents Top users
  1. J

    A slice causes a tennisball to spin and deviate from its normal parabolic path.

    Homework Statement A tennis player slices the ball to spin and deviate from its normal parabolic path. What is an explanation for this phenomenon? I am having trouble visualizing the phenomena that is occurring with the slice and as well as the explanation give by the book. How is the...
  2. M

    How is the Inner Product Expansion in Holomorphic Bundles Derived?

    let x a point on complex manifold X, z_j a coordinate system at x , E a holomorphic bundle and let h_α be a holomorphic frame of E. After replacing h_α by suitable linear combinations with constant coefficients we may assume that h_ α is an orthonormal basis of E_{x}. Then an inner product <h_α...
  3. J

    Why is there no action-reaction pair for normal force?

    Here is an example in which the normal force would not be counted as an action-reaction pair. A 100g block is sitting at rest on a horizontal table. According to Newton's third law, which of the following indicates the correct action-reaction pair of the two forces? So I was stuck between C. The...
  4. N

    Finding normal stress in composite bar

    Homework Statement The 2000 mm long composite bar shown in Fig. 1 consists of an aluminum bar having a modulus of elasticity EAl = 70 GPa and length LAl = 500 mm, which is securely fastened to a steel bar having modulus of elasticity ESt = 210 GPa and length LSt = 1500 mm. After the force P...
  5. B

    How to Handle Non-Normal Residuals in Multiple Regression Analysis

    Hi there, I have performed a multiple regression analysis and I am checking the assumptions. The normal probability plot is not exactly a straight line, but is it okay? If you were looking at the plot would you be satisfied hat the normality assumption is valid...
  6. C

    Finding the product of multiple normal distributions

    Hi all, I've been working on a little side project, but I've hit a road block on the maths for this one. Basically if you imagine a sealed pack of 10 cards, there is a 20% chance that the pack contains one foil (more valuable) card. The mass distribution of the foil cards are (heavier and)...
  7. D

    Normal Mode Analysis at non-equilbrium structures

    Hello, My question stems from a research project of mine involving taking the normal modes of clusters of molecules from a potential. I was curious of the interpretation that can be made of normal mode vectors at a non-equilibrium structure, i.e something following a MD trajectory beginning at...
  8. D

    Normal Mode Analysis at non-equilbrium structures

    Hello, My question stems from a research project of mine involving taking the normal modes of clusters of molecules from a potential. I was curious of the interpretation that can be made of normal mode vectors at a non-equilibrium structure, i.e something following a MD trajectory beginning at...
  9. B

    Generating Probability Resulting in a Normal Distribution

    I'm programming a process that runs in iterations with a probability of stopping at every iteration. As it gets closer to the desired run-time, this probability should increase so that if the process is run many times over, the runtimes will form a normal distribution, with most of them having...
  10. M

    Ultra-high-energy cosmic ray ≠ collision of 2 'normal' rays?

    Hi, I have a rather basic question: most 'cosmic rays' have an energy of about 109 eV, but there are also 'Ultra-high-energy cosmic rays' with an energy of around 1019 eV to 1020 eV, so I was wondering if they couldn't be the result of collisions of two 'normal' cosmic rays that hit each...
  11. T

    Solving Normal Distribution Homework: μ, σ, X, p

    Homework Statement I've attached the question. Homework Equations μ=np and σ=√(np(1-p)) Im using the normal distribution function on my calculator to avoid using z tables The Attempt at a Solution The mean I calculated it to be 160/4 = 40. standard deviation...
  12. M

    Convolution of iid non central Chi square and normal distribution

    Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.
  13. D

    Accelerated Honors vs Normal Calculus

    Hello everyone. I've been looking into joining my university's honors calculus course. I graduated high school with Calc 1, and Calc 2 completed, but I didn't do too well because, I didn't apply myself as much as I should have (senioritis). I received a 3.0 in Calc 1, and a 2.4 in Calc 2. Do you...
  14. R

    Proving the vector OA is normal to the plane OBC

    Homework Statement Given position vectors: OA ( i + 2j - k) ; OB ( -i + 2j +3k); OC ( 2i + j + 4k) Given that OA is perpendicular to OB. The Question : Show that OA is normal to the plane OBC. Homework Equations r . n = d To find the normal of the plane OBC, I used n = BO x...
  15. S

    Normal force of weight on the ground

    Homework Statement If we are simply standing on the ground will our normal force be always equal to our weight besides when we are jumping or when we land on the ground from a fall? When we are in an elevator, will the normal downwards force on the floor be of our weight (cancelling out our...
  16. J

    Normal distribution + calculation of Z values

    For a normal distribution with E[x]=0 and Var(X)=1, how do we determine the Z-value of a particular percentage ? i.e. if the percentage is 5%, how do we know that Z(5%)= 1.645 ? is there a calculation involved or do we get it from observing the x-axis of the normal distribution ?
  17. G

    Flux, how to find n (normal) and derivation of formula?

    Homework Statement Find the flux of the following fields: F_1 = xi + yj F_2 = -yi + xj across the following curve: The circle r(t) = (cost) i + (sint) j t is from [0,2pi] Homework Equations Flux = ∫F dot n ds = ∫M dy - N dx The Attempt at a Solution For F_1 I got: M = x =...
  18. C

    Light waves from a normal house hold globe effecting a dc circuit. Why?

    Hello. I am new to electronics and physics. Since injuring my back at work, I now have a lot of time on my hands to learn about the things that facinate me. So please forgive me for any wrong terminology or spelling and grammar mistakes. I have recently made a small jacobs ladder using a lm555...
  19. A

    Trying to find references for polarization effect of Normal Zeeman Effect

    Hi, I am trying to find a resource that can explain how σ and ∏ lines obtain their polarizations. I have not found resource that actually show the calculation or solid explanation that show this.The references are usually state that σ and ∏ have circular polarization and linear polarization...
  20. onomatomanic

    Involuntary urination as a normal response

    Other than the obvious case of the (real or perceived) pressure of a full bladder eventually becoming unbearable, under what conditions do healthy people, i.e. those who do not ordinarily suffer from incontinence, lose bladder control? I know of two - extreme fear and choking/strangling. In the...
  21. S

    Estimating Variance of Normal distribution.

    Suppose we have a normal distribution and a sample of n values from the normal distribution. To estimate the variance we can use the standard sample variance formula ( average squared distance from the mean divided by either n ( biased estimator ) or n-1 ( unbiased estimator ) ). There is...
  22. C

    Finding Normal Vector and Tangent Plane at a Given Point

    help me find this normal vector! Homework Statement Find a normal vector n and the equation of the tangent plane to the surface S at the point x0 S: z=ln(x2+3y2) x0=(2,-1,ln7) Homework Equations The Attempt at a Solution ok so I have this general formula from the textbook. z=...
  23. J

    Bloch modes and normal waveguide modes- help to clear up

    Hi all, I'm a little confused about Bloch modes vs. waveguide modes of a single waveguide and was wanting some pointers. I read that Bloch modes are results of the wavefunction of a particle (usually, an electron) placed in a periodic potential. In the case where we have an array of cylinder...
  24. W

    Proof of ratio distribution normal and uniform

    Let X be standard normal and Y uniform [0,1] find the distribution of Z=X/Y. i think i managed to deal with this problem up to the integral stage: P(X/Y< t ) = P(X<Y*t ) thought of : 1. F_{z}(t) = \int^{1}_{0}\int^{yt}_{0}f(x,y)dxdy 2. F_{z}(t) = \int^{yt}_{0}f(x)dx maybe is neither one of...
  25. K

    Calculating Risk Function of Normal Distribution Sample

    Homework Statement Let X1,X2 be a random sample of size 2, from a normal distribution with mean μ and σ2=1. Let T=t(X1,X2)=X1+X2 be the estimator of μ and l(t;μ)=t-μ be the loss function. Compute risk function R(μ). Homework Equations R(μ)=∫∫(l(t;μ))∏f(xi;μ)dxi The Attempt at a...
  26. G

    Normal of two tangent circles

    Hey guys, i'm building an apparatus with a sliding pin containing a spring and a ball. I want to lock in two different positions so I've rounded two slots in the housings. I would like to know what is the equation two find the normal force of the spring on the ball depending on the displacement...
  27. N

    Problem involving tangent vector, normal vector, binormal vector and curvature

    Homework Statement r(t)=cos(t)i+sin(t)j+sin(2t)k Find the curvature κ, the unit tangent vector T, the principal normal vector N and the binormal vector B at t=0. Find the tangential and normal components of the acceleration at t=∏/4 Homework Equations T(t)=r'(t)/|r'(t)| N(t)=T'(t)/|T't|...
  28. J

    Constraints on matrix-variate normal distributions

    Hello, all. I'm wondering about matrix-variate normal distributions. I know they normally assume an n x p random matrix, X, and associated row and column covariance matrices Omega and Sigma, but I'm wondering how the probability density function changes if X is comprised of a square...
  29. J

    Finite Order of Elements in Groups with Normal Subgroups

    Proposition: If every element of G/H has finite order, and every element of H has finite order, then every element of G has finite order. Proof: Let G be a group with normal subgroup H. Suppose that every element of G/H has finite order and that every element of H has finite order. We wish to...
  30. J

    If H and K are subgroups of G, and K is normal, then HK is a subgroup of G.

    Ignoring the fact that it is redundant at times, is this proof correct? Also, is there a way to show that same result using the fact that K is closed with respect to conjugates rather than the fact that for all a in G, aK=Ka. Thank you! :) Proposition: If H and K are subgroups of G...
  31. A

    Why does the normal hydrogen atom lack a neutron

    why is hydrogen the only element in the periodic table that lacks a neutron?
  32. I

    Need help in determining normal force the question is from ss krotov

    cylinder of mass m and radius r rests on two supports of same height. one is fixed other slides with velocity v.determine normal force N by the cylinder on stationary support at the moment when distance between the point of contacts A and B of cylinder and support) is r√2assuming supports were...
  33. D

    Points that a curve's normal line intersects

    Homework Statement The line that is normal to the curve x2+2xy-3y2=0 at (5,5) intersects the curve at what other point? 2. The attempt at a solution I differentiated the equation, found the slope of the curve at that point, and I then found the equations for the tangent line and normal...
  34. W

    Multivariate normal distribution , conditional probability problem

    Homework Statement Given X,Y RV both have normal distribution with: μ_{x}=6,μ_{y}=4,σ_{x}=1,σ_{y}=5,ρ=0.1 a. are X,Y independent? b. find P(X≤5) c. find P(Y≤5|X=5) 2. The attempt at a solutiona. no -> ρ=0.1 -> cov(X,Y)≠0 b. define Z=\frac{X-6}{1} ; Z~N(0,1) so P(X≤5) = P(Z≤-1) = \Phi(-1)...
  35. A

    Normal matrix that isn't diagonalizable; counterexample?

    I've been reading that the diagonalizable matrices are normal, that is, they commute with their adjoint: ##M^*M=MM^*##, where ##M^*## is the conjugate transpose of ##M##. So a matrix is diagonalizable if and only if it is normal, see: http://en.wikipedia.org/wiki/Normal_matrix But from...
  36. K

    Finding Normal Vectors to Surfaces of Revolution

    Suppose you have a single variable differentiable function r: R -> R restricted to an interval, like [0,1] for simplicity, if you want. Consider the surface of revolution obtained by rotating the graph of r around the x axis. How do I find the NORMAL VECTOR to the surface at each of its points...
  37. D

    Least squares approximation: Is smaller normal distance always better?

    I took a LA course in the spring, and was interested by the least squares method for building models. I decided to practice this concept by attempting to build a model that would predict ticket sales for the Mega Millions lottery given the jackpot amount. I have 249 data pairs of jackpot and...
  38. A

    Solution to the integral,i.e, expected value of a function of normal variable

    I want to calculate \int_a^b \frac{1}{\sqrt{2 \pi \sigma^2}} e^{(-(x-\mu)/\sigma^2)} log_2 (1 + e^{-x}) dx
  39. E

    Complex Analysis - Normal Families

    Homework Statement Let U be a domain in \mathbb{C} with z_0 \in U. Let \mathcal{F} be the family of analytic functions f in U such that f(z_0) = -1 and f(U) \cap \mathbb{Q}_{\geq 0} = \emptyset, where \mathbb{Q}_{\geq0} denotes the set of non-negative rational numbers. Is \mathcal{F} a normal...
  40. V

    Program that accelerates video play speed and keeps audio at normal pitch

    I've been interested in this function Youtube offers on videos ever since I first used it a few months ago. It's amazing. Some videos are just way too long. The speakers will have something very informative to say, but they'll just ramble and/or speak very slowly. For some reason, Youtube only...
  41. A

    How to calculate normal stress and shear stress on the beams.

    This is the my homework.Who can solve this for me ? i upload my solutions and the problem .Thanks.
  42. K

    Normal reaction, is this a concept we really understand?

    Hi guys ^^ I am still at A level physics, so don't flame me for my lack of knowledge Now i have been taught that for ex: We have a block of wood named A at rest on a perfectly smooth surface. If we analyse a free body diagram, we have a weight mg downwards acting on the block and a normal...
  43. C

    Bivariate Normal Distribution, contour ellipse containing given % samples?

    Given a bivariate gaussian distribution, I'm attempting to find the probability p for which the ellipse of all points (x,y) for which P(X = x, Y= y) = p contains a given % of the samples drawn from the distribution. I want the 2d equivalent for the 1 dimensional case: given a normal...
  44. T

    Two supposedly simple Standard Normal questions

    1) If X~N(μ,σ2, find the value of c in terms of σ such that P(μ-c ≤ X ≤ μ + c) = 0.95 Attempt: Ok so I have a feeling I will eventually need to reference a standard normal table, but I tried to standardize the rv first: P (-1 ≤ (X-μ)/c ≤ 1 ) = 0.95 Now here's where I'm stuck, what...
  45. S

    Determine normal stresses for pure bending moments

    Homework Statement Hi I am having tough time figuring out how to determine normal stresses σx, σy, σz using the flexure formula. All that confuses me is which moment to take for which σ. My for σx or Mz for σx and so on.. I will post an example question. In the question below, find the...
  46. W

    Standard normal distribution help

    Homework Statement Let Z follow a standard normal distribution. Compute E(Z^3) and E(Z^4) Homework Equations I know that mu is 0 and sigma is 1. And f(z) = e^(-z^2/2)/sqrt(2pi) The Attempt at a Solution I tried to take the integral of ∫Z^3 * f(z) from the integral from -∞ to ∞...
  47. A

    How to Deduce the Normal Vector from a Given Vector Equation?

    I'm having trouble finding the equation normal to the plane for part (ii). The vector equation I got for part (i) is r=(1/2,1,2/3) + t(3/2,2,-2/3). How do you deduce the normal vector from this? The answer is the vector (9,12,-4). I've tried anything but don't know where they got this result...
  48. B

    Stoke's theorem and normal vectors

    Stokes' theorem uses the curl of a vector field dotted by the normal vector of a surface...but what happens when you use a larger or smaller normal vector? You get a different answer but the theorem doesn't specify to use the unit normal vector. So which normal is the correct one to use...
  49. V

    Problem about normal subgroups

    Homework Statement If A,B and C are normal subgroups of G where B\subseteqA show that A\bigcapBC=B(A\bigcapC) Homework Equations The Attempt at a Solution Let x\inA\bigcapBC.then x\inA and x\inBC Now as B\subseteqA thus BA=A.thus left side is BA\bigcapBC Dont know how to proceed.
  50. B

    Adding normal distribution - z-scores

    Hi - I have a quick question. I understand that the sum of two normal distributions is a normal distribution. Now let's say I have the z-score from one normal distribution and the z-score of another set of data that is also normally distributed and a third and a fourth etc. I just want...
Back
Top