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.

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  1. karush

    MHB  standard normal sscurve P(Z le t) =0.9

    b 90\% of the insects die after t hours. (i) Represent this information on a standard normal curve diagram, indicating clearly the area representing 90\% (ii) Find the value of \textbf{t}. $P(Z\le t) =0.9\quad Z = 1.282\quad t=57+(4.4(1.282))=62.64$ hours \begin{tikzpicture}[scale=0.6]...
  2. L

    Transforming to a Normal Form (PDE)

    I don't know how to solve for u(x,y) from where I left of after 5.
  3. J

    A Why we can perform normal ordering?

    As explained in the summary, it seems that the commutators of some operators (creation and anihilation) can be ignored when quantising the hamiltonian of the Klein Gordon Field. I wonder why we are allowed to do such a thing. Is that possible because we are solely within a semiquantum...
  4. Shreya

    Tangential & Normal acceleration in Circular Motion

  5. S

    B Continuity correction when using normal as approximation for binomial

    What if the value of X is not integer, such as P(X < 1.2)? a) Will the continuity correction be P(X < 1.2 - 0.5) = P(X < 0.7)? or b) Will the continuity correction be P(X < 1.2 - 0.05) = P(X < 1.15)? or c) Something else? Thanks
  6. karush

    MHB Normal distribution graph P(a<x<b)

    The probability that the lifespan of an insect of this species lies between 55 and 60 hours is represented by the shaded area in the following diagram.\\ Write down the values of a and b. $a=\dfrac{2}{4.4}= 0.455 b=\dfrac{3}{4.4}=0.682]$ ok this was a key to a test question from 2013 but mostly...
  7. M

    Area of interior triangle of pyramid normal to a side length

    This isn't homework, but I figured it's fine if I make it a HW problem and post here (if not, please let me know). Let ##z^*=0## be the vertex of the pyramid, and let ##z^*## run the altitude. It's easy to show the area of the base normal to the altitude is ##A = 4 \left.z^*\right.^2...
  8. Ackbach

    MHB Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples

    $\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Let $S_1^2$ and $S_2^2$ denote, respectively, the variances of independent random samples of sizes $n$ and $m$ selected from normal distributions with means $\mu_1$ and $\mu_2$ and common...
  9. karush

    MHB -7.64 Determine the following standard normal (z) curve areas:

    Determine the following standard normal (z) curve areas: Determine the following standard normal (z) curve areas: a. The area under the z curve to the left of $1.75$ from table $5\ \textit{$z^{*}$} =1.7 \textit{ col } .05 = .9599$ $\textit{ \textbf{$W\vert A$} input }...
  10. M

    I Calculating Covariant Derivative of Riemann Tensor in Riemann Normal Coordinates

    Hello everyone, in equation 3.86 of this online version of Carroll´s lecture notes on general relativity (https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html) the covariant derviative of the Riemann tensor is simply given by the partial derivative, the terms carrying the...
  11. person123

    I Fitting Data to Grafted Distribution

    I have a set of data (representing the strength distribution of samples), and I would like to fit a normal-Weibull grafted distribution. To the left of a specified graft point, the distribution is Weibull, and to the right it's normal. At the graft point, the value and the first derivative are...
  12. S

    Probability related to Normal Distribution

    a) Let X = distance walked on Friday and Y = distance walked on Saturday X ~ N (12, 0.192) and Y ~ N (10, 0.52) Let A = Y - X → A ~ N (-2 , 0.2861) P(Y > X) = P(Y - X > 0) = P(A > 0) = 9.2 x 10-5 But the answer key is 0.026 Where is my mistake? Thanks
  13. bbbl67

    I A large normal atom, but with a muon in its outer shell?

    So let's say we have a large neutral atom, e.g. gold with 79 electrons around it. Let's say we replace its outermost electron with a muon. Muons orbit closer to the nucleus than electrons, much closer. Will the outermost muon be closer into the nucleus than even its innermost ground-state...
  14. S

    Why a normal distribution is not a good approximation for these exam scores?

    I am not really sure what the reason is but my argument would be if normal distribution is appropriate, then almost all the score will fall in the range of μ - 3σ to μ + 3σ For this case, the range of μ - 3σ to μ + 3σ is 26.6 to 118.4 and all the score is unlikely to be within the range. I...
  15. Vash25

    Gravitational potential energy question - normal force on us

    Hi, If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal...
  16. B

    Solving the wave equation for standing wave normal modes

    ## \frac {\partial^2 \psi} {\partial t^2} = v^2 \frac {\partial^2 \psi} {\partial x^2} ## has solution ## \psi (x, t) = \sum_{m=0}^\infty A_m \sin(k_mx + \alpha_m)sin(\omegat + \beta_m) ## The boundary conditions I can discern $$ \psi (0, t) = 0 $$ $$ \frac {\partial \psi} {\partial x} (L, t)...
  17. M

    I Sum independent normal variables

    (I know how to prove it). Prove that a finite sum of of independent normal random variables is normal. I suspect that independence may not be necessary.
  18. S

    B Question about Chi-Square Test Regarding Normal Distribution

    The first step is to group the data and make a table so I can get the observed frequency for each data interval. I did two different groupings (something like 150 - 160 , 160 - 170 , etc and the other is 150 - 170, 170 - 190, etc) and found out that the conclusion of the hypothesis is different...
  19. P

    I Does the Normal contact force act through the centre of mass?

    Consider the following situation: You have 1 rectangular block lying on a table, and an identical block is placed above the block on the table. Now, this new block is constantly pushed to the right, right before it topples off. Consider the torque about an axis passing through the rightmost...
  20. J

    Finding the normal force of a block under water, under pressure

    So since the block is at the bottom there's no pressure pushing it up. To calculate the mass and force of gravity, I multiplied the density of the block by its height and cross sectional area and got 564 kg. Multiplying this by 9.8 I got the force of gravity of 5527.2 N. Now to find the force...
  21. cybernetichero

    COVID Will COVID vaccines become part of normal immunisation regimes?

    I can't post unless I put a message here but my question is pretty clear and there's nothing to add.
  22. H

    Coupled oscillators -- period of normal modes

    Hi, I know there's are 2 normal modes because the system has 2 mass. I did the Newton's law for both mass. ##m\ddot x_1 = -\frac{mgx_1}{l} -k(x_1 - x_2)## (1) ##m\ddot x_2 = -\frac{mgx_2}{l} +k(x_1 - x_2)## (2) In the pendulum mode ##x_1 = x_2## and in the breathing mode ##x_1 = -x_2## I get...
  23. M

    Build a surface normal vector (I use Mathematica)

    Not HW, but seems to fit here. I compute $$n.S = \frac{(-1+\cos(c s))}{c^2} \sin(c s) \neq 0$$ I use the following in Mathematica: r[s_, \[Alpha]_] := Sin[Cos[\[Alpha]] s]/Cos[\[Alpha]] z[s_, \[Alpha]_] := (1 - Cos[Cos[\[Alpha]] s])/Cos[\[Alpha]] x[s_, \[CurlyPhi]_, \[Alpha]_] := r[s...
  24. J

    Forces on a crate with friction: find the normal force

    I have attempted this problem by solving for the normal force. (16.73)(9.8)-51.25(sin)(49.1). I tried to work that out but it was incorrect because apparently the vertical force is zero. Could I get an explanation on what that means and where I should start?
  25. John Greger

    A Obtain Normal Vector of Bubble Wall in Spacetime

    So say I have a bubble embedded in a spacetime with metric: $$ds^2 = -dt^2 + a(t) ( dr^2 + r^2 d\Omega^2_2) $$ how do I compute the normal vector if I assume the wall of the bubble the metric represents follows a time-like trajectory, for any ##a(t)##? Since we are interested in dynamical...
  26. bhobba

    COVID Do People Think It Will Take 7 Years to Get Back To Normal?

    See the following: For what t is worth I think it will be less than 7 years because research is still happening at a breathtaking speed - but exactly when I have no idea. Thanks Bill
  27. A

    MHB Equation of Normal to Curve at (1,5): Solved?

    Really confused bout a question and finding the equation. A normal is drawn at the point (1,5) on the curve defined by the rule y=x2+4. Find the equation of the normal. I substituted the values x=1 and y=5 into the derived equation and got my answer to be x+2y=10? Is that correct?
  28. P

    Gas in mercury manometer, finding its normal volume

    Some notation: - the difference between the heights of mercury, which is effectively the height of the mercury in the open end of the tube is ##h_{diff}## - the volume of gas inside the sealed off end is ##V_{inside}## - the volume of gas when let outside, "normal volume", is ##V_{outside}## -...
  29. S

    Normal force on a rod by the rim of a bowl

    I want to ask the direction of normal force acting on the rod by the rim of the bowl. Is the direction perpendicular to the rod or will it be directed horizontally to the left? My guess would be horizontally to the left because the normal force would be perpendicular to the "plane / surface"...
  30. Eclair_de_XII

    Is it normal for a math student to dislike computational math?

    I know I'm not very good in abstract math, but it still feels more challenging and less mundane than the high school and elementary calculus courses I have been trying to bring myself to review nowadays. Part of me feels complacent about the idea of reviewing stuff I've not touched in quite...
  31. J

    Linear chain of oscillators and normal coordinates

    Hello, I hope the equation formatting comes out right but I'll correct it if not. So far, I have attempted to write ##\ddot{a}_k(t) = \sum_{n}(u^{k}_n)^*\ddot{q}_n(t) ##. Then I expand the right hand side with the original equation of motion, and I rewrite each coordinate according to its own...
  32. SamRoss

    B Simple forces described in terms of fundamental forces

    My first question is actually, what happens when any two objects get near each other? This question is often phrased as "Why can't you really touch anything?" or "Why can't you walk through walls?" I have heard two answers: 1. the repulsion between electrons 2. the Pauli exclusion principle...
  33. J

    B Why are serrated knives more effective than normal knives?

    What physical processes does serration take advantage of that make cutting something with a serrated knife more effective than cutting something with an ordinary knife? What is the optimal shape of each tiny segment of a serrated knife? Would cutting effectiveness increase as you add more...
  34. W

    [Statics] Determining the normal force at an internal point of a member

    For this problem (see image), I get the correct answer for the normal force at point E if I: 1) divide the frame into members AB and CB, 2) solve for the x and y components of the reaction force at point B, 3) make a free body diagram with the cut at point E forming member EB and setting the sum...
  35. B

    Is friction really always related to the normal force?

    What I know is that the force of friction and the normal force are the components of a contact force. So force of friction is related to the contact force. Friction is also related to the normal force by equation ##F_t= μ\cdot N##. In this case (because the block is not moving) N=0 and...
  36. Q

    Normal Stress in Rods Experiencing Temperature Changes

    Now here is the part where I'm sort of stumped myself: Could someone let me know if my reasoning is valid? The professor explained it during office hours and all I got out of that was that something cancels out and the answer is 0.
  37. F

    Refining a normal series into a composition series

    Attempt: Consider an arbitrary normal series ##G = G_0 \ge G_1 \ge G_2 \ge \dots \ge G_n = 1##. We will refine this series into a composition series. We start by adding maximal normal subgroups in between ##G_0## and ##G_1##. If ##G_0/G_1## is simple, then we don't have to do anything. Choose...
  38. F

    Normal series and composition series

    Attempt so far: We're given that ##G## and ##H## have equivalent normal series $$G = G_0 \ge G_1 \ge \dots \ge G_n = 1$$ and $$H = H_0 \ge H_1 \ge \dots \ge H_n = 1$$ We can assume they have the same length because they are equivalent. I think from here I need to construct two composition...
  39. F

    Normal group of order 60 isomorphic to A_5

    Proof: We note ##60 = 2^2\cdot3\cdot5##. By Sylow's theorem, ##n_5 = 1## or ##6##. Since ##G## is simple, we have ##n_5 = 6##. By Sylow's theorem, ##n_3 = 1, 4, ## or ##10##. Since ##G## is simple, ##n_3 \neq 1##. Let ##H## be a Sylow ##3## subgroup and suppose ##n_3 = 4##. Then ##[N_G(H) : G] =...
  40. D

    Three independent random variables having Normal distribution

    Let ##X_1 X_2 X_3 ## be three independent random variables having Normal(Gaussian ) distribution, all with mean ##\mu##=20 and variance ##\sigma^2##=9. Also let ##S=X_1+ X_2 +X_3## and let ##N## be the number of the ##X_i## assuming values greater than 25. ##E\left[N\right]##=? I did not...
  41. N

    I Stern-Gerlach w. normal distribution if magnets were more separated?

    Just wondered if the power of mags. is decreased, or they are more separated, don't you get a normal distribution ? (I'm in biology) - would you also not have predicted that w. reasonably strong magnets, they will either end one one side or the other ? Thx a lot!
  42. mktsgm

    Medical How are normal values of blood pressure and glucose determined?

    Blood glucose is measured and compared against a set of standard/normal values (like, fasting 100 mg/dL etc) to determine if a person has hyperglycemia or not. Similarly Blood pressure readings (systolic & diastolic) are also compared against another set of standard/normal values like 120/80...
  43. Like Tony Stark

    Direction of the normal force when acting on a tilted object

    My question is: given a rigid body which interacts with a surface, what's the direction of the normal force? Because, as the word says, it has to be normal to the surface. But when treating problems of a vertical rod which is slightly pushed and forms an angle ##\theta## with the surface, some...
  44. LCSphysicist

    Spring constant matrix and normal modes (4 springs and 3 masses)

    We need to find the normal modes of this system: Well, this system is a little easy to deal when we put it in a system and solve the system... That's not what i want to do, i want to try my direct matrix methods. We have springs with stiffness k1,k2,k3,k4 respectively, and block mass m1, m2...
  45. person123

    I Normal Stress Vectors: Sketch 1 vs Sketch 2

    Let's say you have a material element with normal and shear stress. These stresses were computed using stress transformation. When the material deforms, should the normal stress vectors remain normal to the surface (sketch 1) or parallel to the other surface (sketch 2)? Which would be more...
  46. LCSphysicist

    Total energy of the normal mode on a string

    What you think about this question? Seems a little strange to me, that is, it considers the maximum kinetic energy when the displacement of the oscillators is maximum, i don't think this is right.
  47. Leo Liu

    Normal force acting on a block on an accelerating wedge

    We have a wedge whose surface is ##\theta## from the horizontal surface. After a block is placed on its frictionless slant surface, the wedge starts to accelerate due to a force F. What is the normal force acting upon the block? I have been trying to solve it but I got no clue. Could someone...
  48. J

    I Normal modes of vibration from the total energy

    A mass ##m## is restricted to move in the parabola ##y=ax^2##, with ##a>0##. Another mass ##M## is hanging from this first mass using a spring with constant ##k## and natural lenghth ##l_0##. The spring is restricted to be in vertical position always. The coordinates for the system are ##x##...
  49. LCSphysicist

    Why Do mω²xa and 2kxa Both Act in Normal Modes Oscillations?

    I am not sure if i get this part of a book i am using: Why are the mwo²xa acting too? Is not 2kxa enough?
  50. tomdodd4598

    I Argument for Existence of Normal Coordinates at a Point

    Hey there, I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here (26:33 - 35:40). In short, the argument goes as follows (I think): we have some generic metric ##{ g...
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