What is Dot: Definition and 562 Discussions

The Red Dot Design Award is a German international design prize awarded by Red Dot GmbH & Co. KG. There are prize categories for product design, brands and communication design, and design concept. Since 1955, designers and producers can apply for the prizes, with the winners being presented in an annual ceremony. Winning products are presented among others in the Red Dot Design Museum on the premises of the historical Zollverein Coal Mine Industrial Complex in Essen. The Red Dot Design Museum Essen, the first Red Dot Design Museum, was built in 1997. The second Red Dot Design Museum was built in Singapore in 2005. The Red Dot Design Award had more than 15,500 submissions from 70 countries in 2014, and in 2016 alone, 1,559 Red Dots were awarded, 102 of them in the "Best of the Best" category.

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  1. M

    I Simple dot product in polar coordinates

    Let's take two orthogonal curves in polar coordinates of the form ##\langle r,\theta \rangle##, say ##\langle r,0\rangle## and ##\langle r,\pi/2\rangle##. Cleary both lines are orthogonal, but the dot product is not zero. This must be since I do not have these vectors in the form ##\langle...
  2. thee qs

    Magnetic moment and magnetic field and dot product

    Homework Statement a magnetic moment of U = 1 (i) + 2 (k) , surrounded by a magnetic uniform field of B= 3 (i) + 4 (j) - 1 (k) find the potential energy in mJ ? Homework Equations dot product of 2 vectors ( ui*bi)+(uj*bj)+(uk*bk) = or finding the module of both vector and doing AB...
  3. S

    B Ambiguity w/ Newton's dot notation + vector-magnitudes

    Stumbled on a potential pitfall that can arise if you combine Newton's overdot notation (for time-derivatives) with boldface/non-boldface notation for vectors/vector-magnitudes. Say you have ##\textbf{v}## for velocity and ##\dot{\textbf{v}}## for acceleration. Speed is then ##v## (magnitude of...
  4. D

    I Differentiating vector dot product

    Hi. If I have a vector v , say for velocity for example then v.v = v2 and I differentiate wrt t v.v I get 2v.dv/dt but if I differentiate v2 I get 2v dv/dt but v.dv.dt is not the same as v dv/dt so what am I doing wrong ? Thanks
  5. Van Ladmon

    Information loss when taking the dot product of vector equations

    Homework Statement Is the following conclusion correct? Assume there's an equation with vectors on both sides. Taking the dot product of this equation with vectors on both sides loses information, but information will not lose when taking dot products with higher rank tensors on both sides...
  6. Shadow89

    Collimated light from red dot scopes?

    I am trying to piece together how the parabolic mirror manages to reflect the "red dot" from the focal point to the eye without distortion. I compare this with a conventional car headlight, which operates almost exactly the same way, except it has a non-transparent backing. Why does the ret dot...
  7. C

    Electron dot structure, Lewis structure

    Which is more correct, teaching the first two valence electrons as paired in the electron dot structure or teaching them as not pairing until forced.
  8. O

    Confused about dot product step while deriving the Liouville equation

    So, while textbook was deriving Liouville eq, this is one of step the book uses. I don't understand this step at all. Why is this step true?
  9. U

    I Question: Quantum Dot Laser - Energy Band

    Hello I am new here, so it's nice to meet you. I study quantum dot lasers and there is something I don't understand about the energy band diagram. Quantum dots are formed with the Stranski- Krastanov method. For example small InGaAs islands of quantum dots are created on a substrate of InGaAs...
  10. G

    Intersecting 2 continuous laser in thin air to create a dot

    I am planning on making an experiment about intersecting continuous wave laser from 2 or more source on 1 point in thin air. The laser i am planning to use is the simple laser diode, pumped with continuous wave, instead of using pulsed wave as in the usual laser pointer as i don't need it to...
  11. Marcin H

    Mutual Coupling & Dot Convention

    Homework Statement Homework Equations KVL and KCL The Attempt at a Solution I am very confused by the dot convention and how it works when writing your loop equations... I can't find any good videos or explanations online and I am completely lost with this dot convention. So I understand...
  12. N

    I Homomorphism of an elementwise sum and dot product

    ∑ab is needed but is impractical to implement. Specifically ∑i ai.10i-|i| in any form where I can work with ∑i ai = α and ∑i 10i-|i| separately. Is there a homomorphic function I can run it through such that ∑ab can be expressed as ∑a∑b? Note: for current problem i cannot simply set it up...
  13. kolleamm

    B Pale Blue Dot Project: Img. Earth-Like Planet w/ 18" Mirror?

    Apparently there's something called the pale blue dot project that needs funding to image an Earth like planet in a nearby star system. I asked them of the lens diameter and they replied that the telescope will use a 18" mirror. Is that enough resolution wise? Seems a little small when you...
  14. lawlieto

    I Inner Product vs. Dot Product Confusion in Quantum Physics?

    I started learning quantum, and I got a bit confused about inner and dot products. I've attached 2 screenshots; 1 from Wikipedia and 1 from an MIT pdf I found online. Wikipedia says that a.Dot(b) when they're complex would be the sum of aibi where b is the complex conjugate. The PDF from MIT...
  15. L

    Vector dot product and parallel vectors

    Homework Statement show that points P, Q and R are in a straight line P (1, -3, 4) Q ( 2, 2, 1) R (3, 7, -2) and find the vectors ## \vec{PQ} ## and ## \vec{QR} ## Homework EquationsThe Attempt at a SolutionIn proving that the points are in a straight line, we might be able to use dot product...
  16. J

    8*8 blue dot matrix led display's specifications

    Hey, I want to ask you about the array led component: 1.9mm(0.8’’)8*8 blue dot matrix led displays (model no:KWM-20882XBA). << Edit by Mentor to add link to datasheet >> https://cdn-shop.adafruit.com/datasheets/956datasheet.pdf I saw the technical data sheet but I couldn’t find the...
  17. Z

    Dot Product of Streaming vectors

    Hi all, Suppose we have vectors coming in order as A, B and then C (but A must be deleted before C comes in). Then how to get the dot product between A and C? It is allowed to store some calculations of A before deleting elements of A, for example, we could store norm of A, dot(A, B) and etc...
  18. R

    Dot Product: Understanding and Solving with Vectors | Homework Help

    Homework Statement Im given vectors: b = x hat + y hat c = x hat + z hat Homework Equations http://imgur.com/a/iHTOT The Attempt at a Solution so I have 2 eq's... one says: r * s = rscos(theta) the other is a summation saying multiply x component 1 with x component 2, add y component 1...
  19. R

    I Why is the dot product equivalent to matrix multiplication?

    Why is the dot product equivalent to the matrix multiplication of its components? I've seen some proofs using Pythagorean and cosine law but they don't give you an intuitive feel as to why matrix multiplication works. The geometric definition (##ab cosθ##) is very easy to understand. To a...
  20. Wrichik Basu

    B What is the real life utility of the dot product and cross product

    Today, my teacher asked us what is the real life utility of the dot product and cross product of vectors. Many of us said that one gives a scalar product, and one gives a vector product. But he said that, that was not the real life utility of the dot and cross product. He asked us, "Students...
  21. Experience111

    A 4th order tensor inverse and double dot product computation

    Hi everyone, I am currently working on a subject that involves a lot of 4th order tensors computations including double dot product and inverse of fourth order tensors. First the definitions so that we are on the same page. What I call the double dot product is : $$ (A:B)_{ijkl} =...
  22. andylatham82

    I How to find angle between vectors from dot and cross product

    Hi, hopefully a quick question here...how do you calculate the angle between two vectors if the only information you have is the value of their scalar product and the magnitude of their cross product? Thanks! Andy
  23. bluejay27

    I Emitting light to a Quantum dot

    When visible light is being emanated to a quantum dot, why is it that you can see specific colors? I am not talking about the fluorescence that would occur when UV light is emanated.
  24. bluejay27

    B Quantum Dot Emission: Band Gap & Heisenberg's Uncertainty

    Why does the quantum dot's band gap increase as in shrinks in size? What is the principle behind this? Is the Heisenberg's uncertainty principle?
  25. V

    Mathcad dot or dashed notation

    Hi, I have a long differential equation which I am typing into mathcad. I want to use either dot or dashed notation instead of d/dt to shortern it and make it more readable. Do you know how I can do this so that it actually recognises it as a derivative? I
  26. F

    I Notations used with vector field and dot product

    Hello, I try to understand the following demonstration of an author (to proove that dot product is conserved with parallel transport) : ------------------------------------------------------------------------------------------------------------------------ Demonstration : By definition, the...
  27. F

    I Conservation of dot product with parallel transport

    Hello, I have 2 questions regarding similar issues : 1*) Why does one say that parallel transport preserves the value of dot product (scalar product) between the transported vector and the tangent vector ? Is it due to the fact that angle between the tangent vector and transported vector is...
  28. mamadou

    I How do we compute an integral with a dot product inside ?

    I was trying to solve a problem involving work , as we know : w = \int_{a}^{b} \vec{f}.d\vec{s} but in my problem the path was cyrcular , so how to evaluate this kind of integral ?
  29. donaldparida

    Dot between the molecular formula of compounds

    I have seen many instances of molecular formulas of two or more compounds with a dot between two adjacent molecular formulas like CuSO4.10H20, CaCO3.MgCO3, K2SO4.Al2(SO4)3.24H20 and so on. What does the dot indicate?
  30. bluejay27

    I What is the maximum size of a Quantum Dot?

    What is the maximum size of a Quantum Dot? What are the limits of the size of the quantum dots? At what size do we stop calling a Quantum Dot a Quantum Dot?
  31. A

    I Is the Dot Product of Unit Vectors Related to Magnitudes and Angle Between Them?

    Okay so I understand that in order to represent a vector which is in cartesian coordinates in spherical coordinates.. we use the transformation which is obtained by dotting the unit vectors. So my question goes like this: when we dot for example the unit vector ar^ with x^ we obtain sin(theta)...
  32. A

    I Exploring Effective Mass and Spin-Orbit Interactions in Semiconductor Physics

    Often I see people using an effective mass model to describe electrons in the bottom of the conduction band. Spin orbit is then included as a perturbation in this effective mass model. But what is the justification for using this sort of model? Would the correct way not be to start from the full...
  33. P

    Find X Coord of Point A in Dot Product Homework

    Homework Statement How would I find the X coordinate of point A. So far I have: A: ( X=? Y=-231.125" Z=175") B: (X=0" Y=0" Z=144") https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/90/90134-44f7db5f8e2c5989352d374160952d17.jpg Homework Equations...
  34. R

    Classical Book on Cross and Dot products

    I had a book on dot and cross products, and the author presented his material in terms of Maxwell's equations. It's a popular book. Alas, I can't remember the title or author. I was going to loan it to a friend but found the book missing. The book isn't long at all and is a paperback book...
  35. T

    I Dot product constrained optimization

    Problem: Fix some vector ##\vec{a} \in R^n \setminus \vec{0}## and define ##f( \vec{x} ) = \vec{a} \cdot \vec{x}##. Give an expression for the maximum of ##f(\vec{x})## subject to ##||\vec{x}||_2 = 1##. My work: Seems like a lagrange multiplier problem. I have ##\mathcal{L}(\vec{x},\lambda)...
  36. S

    A Probability of photon emission from quantum dot

    Hi guys, I am looking for a formula which I am sure exits but I cannot locate it. The problem is that a quantum dot absorbs a photon of wavelength λ0(dot is semiconductor or could be any other material). Assuming that it reemits a photon, what is the probability that this emitted photon will...
  37. nehCrM

    I Electron configuration vs. Lewis dot structure?

    I am trying to make a connection between the two in terms of the electron configuration for an atom relative to the octet rule for Lewis Dot diagrams. Maybe I just don't understand what the electron configuration represents. Why is it that Lewis Dot diagrams utilize 8 valence electrons as a full...
  38. A

    I K dot p method with SO interaction

    I am trying to derive the k dot p formula with the spin orbit interaction term included. I am having some trouble. I insert a bloch wave function multiplied with an unspecified spinor. But how do I treat the cross product term that comes from the SO and what is the effect of the pauli matrix...
  39. parshyaa

    I Define Dot Product: A.B = ||A|| ||B|| cos(theta)

    I have seen a proof for the formula of A.B = ||A|| ||B|| cos(theta)[ proof using the diagram and cosine rule]. In the proof they have assumed that distributive property of dot product is right. diagram is given below c.c =(a-b).(a-b) = a^2 +b^2 -2(a.b) [ here they used distributive law] I...
  40. parshyaa

    I Why is A.A = ||A||^2 in Vector Analysis?

    Why A .A =||A||^2(dot product) in vector analysis. Every where in vector analysis mathematicians used this result. To prove A.B = ||A|| ||B||cos(theta) we assume that A.A is ||A||^2 , without assuming this we can't prove A.B = ||A|| ||B||cos(theta) . I think they assumed it because dot product...
  41. Clever Penguin

    B Pale Red Dot Mission: Launching Probes to Alpha Centauri in 2030s

    Mission objective: Send a spacecraft to the Alpha Centauri star system and collect data People behind the mission: Mark Zuckerberg, Stephen Hawking, Martin Rees, Pete Worden, Avi Loeb, Freeman Dyson, Lou Friedman, Saul Perlmutter, Philip Lubin, Santa Barabara. Estimated mission launch: 2030s...
  42. S

    How to Determine Perpendicular and Collinear Vectors with 2 Variables

    Homework Statement This problem actually has 2 parts. For vectors a= (2,p,8) and b= (q,4,12), determine the values of p and q so that the vectors are a)perpendicular b) collinear textbook answer: a) p= 1 and q= -50 (answers may vary) b) p= 8/3 and q=3 Homework Equations a*b = 0 a*b =...
  43. Jatin Kaushal

    B Why do we put the dot multiplication symbol when integrating

    This is I think a really dumb question, but I never got it, why do we have that dot symbol when we integrate. Like in gauss's law, we have ∫E⋅dA . why is that ⋅ there? Thank you for your help
  44. H

    Dot product of tensor-vector product

    Homework Statement Using index notation only (no expanding of terms), show: \begin{equation*} \text{(a) }\underline{ \bf{a}} \cdot \underline{\bf{A}} \underline{\bf{b}} = \underline{\bf{A}} \cdot \underline{\bf{a}} \otimes \underline{\bf{b}} \end{equation*} Homework Equations...
  45. A

    Finding the Locus of a Moving Point: Solving for a Hyperbola Using Dot Products

    Homework Statement A point P moves so that its distances from A(a, 0), A'(-a, 0), B(b, 0) B'(-b, 0) are related by the equation AP.PA'=BP.PB'. Show that the locus of P is a hyperbola and find the equations of its asymptotes. Homework EquationsThe Attempt at a Solution AP.PA' =...
  46. T

    B Voyager 1 - image of 'Pale Blue Dot'

    Please could someone explain why Earth looks to bright when it is so far away? Also, why can't we see any other objects (other planets and stars) in the image? Thank you.
  47. M

    Using the complex susceptibility in E dot J

    Homework Statement Use the complex susceptibility to prove that the dot product of E and J is related to the absorption term (the imaginary part - χ'') and independent of the real part (χ'). It is also stated that in order to do is, assume monochromatic field and take the absorption time...
  48. S

    Gradient of dot product using suffix notation

    Homework Statement Find the gradient of \underline{\nabla}(\underline{a}\cdot\underline{r})^n where a is a constant vector, using suffix notation and chain rule. Homework Equations On the previous problem,s I found that grad(a.r)=a and grad(r)=\underline{\hat{r}} The Attempt at a Solution...
  49. Z

    Understanding the Relationship between Dot and Cross Products

    Homework Statement Find (u• v) 2 + ||u × v||2 , given ||u|| = 5 and ||v|| = 3 Homework Equations u•v=||u|| ||v|| cos(x) u×v=||u|| ||v|| sin(x) The Attempt at a Solution Using these two equations I squared them both, brought them together and ended up with 225cos2(x) + 225sin2(x) and received...
  50. O

    Derivative of Dot Product via Product Rule, commutative?

    Homework Statement Basically, I'm looking at the property that says if the magnitude of a vector valued function is constant, then the vector function dotted with it's derivative will be zero. But I'm stuck towards the end because the proof I found online seems to skip a step that I'm not...
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