Unity Definition and 127 Threads

Unity is a cross-platform game engine developed by Unity Technologies, first announced and released in June 2005 at Apple Inc.'s Worldwide Developers Conference as a Mac OS X-exclusive game engine. The engine has since been gradually extended to support a variety of desktop, mobile, console and virtual reality platforms. It is particularly popular for iOS and Android mobile game development and used for games such as Pokémon Go, Monument Valley, Call of Duty: Mobile, Beat Saber and Cuphead. It is cited to be easy to use for beginner developers and is popular for Indie game development.The engine can be used to create three-dimensional (3D) and two-dimensional (2D) games, as well as interactive simulations and other experiences. The engine has been adopted by industries outside video gaming, such as film, automotive, architecture, engineering and construction.
Several major versions of Unity have been released since its launch. The latest stable version, 2021.1.0 , was released on 23 March 2021 (23 March 2021).

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  1. M

    Are these values of the following correct? (Complex cube root of unity)

    Given that x is a complex cube root of unity, we have ## x^{3}=1 ## but ## x\neq 1 ##, where the cube roots of unity are ## 1, \omega, \omega^2 ## and ## \omega, \omega^2 ## are the imaginary roots such that ## \omega^3=1, 1+\omega+\omega^2=0 ##. Now we will consider three cases of the...
  2. M

    Voltage regulation in transformers at unity power factor

    So I've done part a) Primary current = 200000/415=481.9 Cos θ = -0.8 Sin θ = 0.6 Reg=(481.9 ( 0.014*-0.8 + 0.057*0.6))/415 = 0.0267 Reg% = 2.67% Part b I simply used the same equation but for secondary: @ unity p.f., cos θ =1, sin θ = 0 secondary current = 200000/11000 = 18.18...
  3. S

    I Problems with understanding the role of the partition of unity

    I'm reading "Calculus on manifolds" by Spivak and i can't understand the role that the partition of unity play and why this properties are important , Spivak say: What is the purpose of the partition of unity? if someone can give me examples, bibliography or clear my doubt i'll appreciate it.
  4. BasNijhof

    Is there a way to calculate the Drag coefficient from any given object?

    Hi guys, for my final high school project I want to create a simulation in Unity (A game engine) in which you should be able to make an airplane fly with extremely accurate physics. In the regular formula for Drag is: Fd = 1/2 * ρ * v^2 * Cd * A. I can get all these things except the Drag...
  5. M

    A Eric WEinstein's Geometric Unity theory

    Eric Weinstein finally released a video of his 2013 Oxford talk on "geometric unity". There are many fans and skeptics out there, looking in vain for a genuinely informed assessment of the idea. I admit that so far I have only skimmed the transcript of the video, being very pressed for...
  6. AutGuy98

    MHB Find n such that the group of the n-th roots of unity has exactly 6 generators

    Hey guys, Sorry that it's been a decent amount of time since my last posting on here. Just want to say upfront that I am extremely appreciative of all the support that you all have given me over my last three or four posts. Words cannot express it and I am more than grateful for it all. But, in...
  7. AutGuy98

    MHB Prove that the 12-th roots of unity in C form a cyclic group

    Hey guys, Sorry that it's been a decent amount of time since my last posting on here. Just want to say upfront that I am extremely appreciative of all the support that you all have given me over my last three or four posts. Words cannot express it and I am more than grateful for it all. But, in...
  8. S

    Scattering from lossy medium whose refractive index is unity

    Consider a thin transparent plate surrounded by air. The plate's refractive index is exactly the same as the air's, but it does have a small loss (say of the order of 1%). Let the plate be vertical and normal to our "page" or your computer screen. A laser beam passes through the plate at an...
  9. Mr Davis 97

    Prove that the roots of unity is a cyclic group

    Homework Statement Let ##\mu=\{z\in \mathbb{C} \setminus \{0\} \mid z^n = 1 \text{ for some integer }n \geq 1\}##. Show that ##\mu = \langle z \rangle## for some ##z \in \mu##. Homework EquationsThe Attempt at a Solution My thought would be just to write out all of the elements of ##\mu## in...
  10. Russell Patterson

    Insights Orbital Mechanics in Unity Game Engine for Augmented Reality - Comments

    Greg Bernhardt submitted a new PF Insights post Orbital Mechanics in Unity Game Engine for Augmented Reality Continue reading the Original PF Insights Post.
  11. W

    What circuit element should be placed in series to raise power factor?

    Homework Statement A series circuit has an impedance of and a power factor of 0.720 at 50.0 Hz. The source voltage lags the current. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor? Homework Equations cosΦ=R/Z...
  12. M

    B Is there a unity across scale in the universe?

    Is our concept of scale, of micro and macro, of quantum and cosmic, relative to our perception as humans? If General Relativity and Quantum Physics both yield truth, then perhaps it is an error in human cognition that seems to perceive a disconnect between the two. The universe is just the...
  13. Mr Davis 97

    Every ring with unity has at least two units

    Homework Statement T/F: Every ring with unity has at least two units Homework EquationsThe Attempt at a Solution I thought that the answer was true, because if a ring ##R## has unity ##1##, then ##1 \cdot 1 = 1## and ##(-1) \cdot (-1) = 1##. Where am I going wrong?
  14. H

    Second order low pass filter with unity gain

    Homework Statement I need to design a second order filter with unity gain. Homework Equations None - not taking component values into account for now. The Attempt at a Solution Is this a correct method of creating a 2nd order low pass filter with unity gain?
  15. PsychonautQQ

    Extending a field by a 16th primitive root of unity

    Homework Statement let c be a primitive 16th root of unity. How many subfields M<Q(c) are there such that [M:Q] = 2 Homework EquationsThe Attempt at a Solution I think the only subfield M of Q(c) such that [M:Q] = 2 is Q(c^8). Then M = {a+b(c^8) such that a,b are elements of Q}. I'm thinking...
  16. R

    How Do You Calculate Capacitance for Unity Power Factor in a Single-Phase Motor?

    Homework Statement Not sure if this is the correct place for Electrical Engineering Homework help but here goes A single-phased motor connected across a 240-V source at 50Hz as shown in the figure has a power factor of 1.0, I = 20A, I1 = 25 A. Find the capacitance required to give a unity...
  17. M

    MHB Principle Ideal in F[x] & Primitive nth root of unity

    Let ζ5 be e2πi/5. Find a monic polynomial of degree two in K(ζ + ζ−1) So, if E/F is a field extension, with α∈E then K(α) = {f(x)∈F[x] | f(α)=0} and m(x) is the minimal polynomial of α over F such that K(α) = [m(x)] where [m(x)] is the ideal generated by m(x). I was thinking maybe (x- ζ -...
  18. Anithadhruvbud

    Can refractive index of a material be less than unity?

    And what is the difference between refractive index and absolute refractive index? Why do we use relate two absolute refractive index to find the refractive index of a particular material say we need to find refractive index of water with respect to ice.and why do we always put the higher value...
  19. D

    Why is the active mass of solids taken as unity?

    Homework Statement I understood the fact that since the density of solids and liquids remain constant in a reaction therefore the active mass must be a constant.But why is it that we take it as unity. Is is some kind of coonverntion,or is there a reason behind it? Homework EquationsThe Attempt...
  20. K

    MHB Find Min Polynomial of $\alpha$ Over $\mathbb{Q} | Solution Included

    I started by setting $\alpha= e^{2\pi i/3} + \sqrt[3]{2}.$ Then I obtained $f(x) = x^9 - 9x^6 - 27x^3 - 27$ has $\alpha$ as a root. How can I proceed to find the minimal polynomial of $\alpha$ over $\mathbb{Q},$ and identify its other roots?
  21. ichabodgrant

    Decomposition using roots of unity

    Homework Statement Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity. Homework Equations As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots. The Attempt at a Solution [/B] So, let ω = e2πi/5. I can therefore find all the 5th...
  22. J

    Usefulness of partition of unity?

    I am going through Spivak's Calculus on manifolds. I am on the chapter now regarding partitions of unity. I understand the construction of it, but why exactly is a partition of unity useful? Why do we care about it?
  23. A

    The sum of angles in 3D is not 90 while in 2D it is?

    Sorry for the confusing tittle but I could not explain it better. Here is what I am trying to ask: When you have 2 axis(x and y) such as the image below, the sum of the two angles, a and b will always be equal to 90 degrees. a + b = 90degrees However when you add a 3rd axis(x, y and z, making...
  24. PcumP_Ravenclaw

    Roots of unity, Roots of complex equations of the form z^n = 1

    Dear all, please see the page above, (Alan F, Beardon, Abstract Algebra and Geometry). On the page, Theorem 3.5.2 says that the set of Complex numbers from ## z^n = 1 ##, where ## |z| = 1 ## forms a group w.r.t multiplication. I want to know if... The inverse of all elements...
  25. Ramana

    Unity Gain Buffer with Op-Amp 741 for LVDT Sensor

    Hello, Here need a suggestion on Unity gain buffer using op-amp 741. The output i need in the range according to change in LVDT sensor (resistive type). The output of the sensor is 35mv to 3.5 VDC. The circuit i build using op-amp741 as voltage follower where the output is given feedback to...
  26. M

    Internal semidirect product and roots of unity

    Homework Statement Let ##G=G_{12}##, ##H_1=G_3##, ##H_2=G_2##. Decide if there are groups ##K_1##, ##K_2## such that ##G## can be expressed as the internal semidirect product of ##H_i## and ##K_i##.The Attempt at a Solution Suppose I can express ##G_{12}## as an internal semidirect product...
  27. G

    Ring Theory Problems: Unity vs. Non-Unity

    Dear Friends, Please tell me the differences created in ring theory problems when 1.Unity is taken in integral domains. 2. Unity is not taken in integral domains. Do results become more general in the second case. Why one standard way not adopted worldwide by all authors because...
  28. M

    Calculating and Graphing the 4th Root of -4

    Hello everyone. How to find the 4th root of -4? I know it's just plugging in the number into the formula but how since n=4, how can we calculate that without calculator? And how to draw it? Here I attached what I have done so far.
  29. Saitama

    MHB Cube root of unity with a huge exponent

    Problem: Let $y=x/(1+x)$, where $$\Large x=\omega^{2009^{2009^{\cdots \text{upto 2009 times}}}}$$ and $\omega$ is a complex root of 1. Then $y$ is A)$\omega$ B)$-\omega$ C)$\omega^2$ D)$-\omega^2$ Attempt: I somehow need to show that the huge exponent is of the form $3k$, $3k+1$ or $3k-1$...
  30. J

    How can I evaluate f(x) based on Theorem 3?

    Homework Statement In F17, 2 is a primitive 8th root of unity. Evaluate f(x) = 7x3+8x2+3x+5 at the eight powers of 2 in F17. Verify that the method requires at most 16 multiplications in F17. Homework Equations You can can more clearly see the theorem on page 376-378 and the problem is on page...
  31. mesa

    Question about nth root of unity

    Homework Statement Determine the nth roots of unity by aid of the Argand diagram...Homework Equations Is the nth root of unity where we have a complex number to the 'nth' power equal to 1? For example, $$(2+i)^n=1$$ The Attempt at a Solution None yet, still trying to translate the question.
  32. M

    Commutative rings and unity element proof

    So this is a review problem in our book I came across and i really want to understand it but I am just not having any luck, I did some research and found a guide on solving it but that's not really helping either. We didn't talk about unity elements in class and there aren't any examples in our...
  33. F

    Roots of Unity: Finding Primitive Root W6 and Solving for 1/W6

    Homework Statement Hello everyone, In this problem, I was to mark all the sixth roots of 1 in the complex plane. Then, I was to figure out what the primitive root W6 is. However, I am stuck by the question: "Which power of W6 is equal to 1/W6?" Homework Equations See Below The Attempt at a...
  34. S

    How Do I Design a Unity Gain Amplifier for a Sample and Hold Circuit?

    I need to design a unity gain amplifier for a sample and hold circuit. I've decided to use the circuit shown in the attachment. Now I know the gain = 0.5(Gm2*R1)[(Gm3*R2)/(1 + Gm3*R2)]. The 2N7000 has a Gm of 0.1, so that gets me the values of R1 and R2. I don't know if these are good values to...
  35. B

    Distance between n-th Roots of Unity

    Homework Statement *Find the distance between 1 and the various n-th roots of unity - denoted d(k) *Find a formula for the sum of distances between 1 and each of the n-th roots of unity - denoted S(n) *Find the limit as n->infinity of (1/n).S(n) Homework Equations *The n-th roots...
  36. P

    MHB The Strange Behaviour of Numbers Close to Unity

    I have been looking at material properties such as thermal expansion of metals which usually involves very small coefficients. The general equation of thermal expansion is usually L_\theta = L_0 ( 1 + \alpha \theta) where L is the length and theta is the temperature change. The coefficient...
  37. J

    Understanding Roots of Unity: Proving Even Distribution with Math

    I don't understand why roots of unity are evenly distributed? Every time when we calculate roots of unity, we get one result and then plus the difference in degree, but I think this follows the rule of even distribution and I don't understand that, it is easy to be trapped in a reasoning cycle...
  38. I

    Fixing the Constants of Equations to Unity

    So I was revising elementary classical physics and Newton's equations of motion. When you apply a force on an object in free space, far from gravitational fields, you find that the object accelerates. By conducting experiments where you vary the force or the mass and look at the acceleration...
  39. F

    Does Zp Contain Primitive Fourth Roots of Unity?: Investigating p

    Homework Statement p prime, If p=1 ( mod 3) then Zp contains primitive cube roots of unity. Now I am considering which p does Zp contains primitive fourth roots of unity. opposite way? I mean if p=1(mod4) then Zp contains primitive fourth roots of unity?? 2. The attempt at a solution I...
  40. A

    Adding primitive roots of unity

    Homework Statement I was trying to figure out whether or not ##\zeta_5 + \zeta_5^2## and ##\zeta_5^2 + \zeta_5^3## were complex (where ##\zeta_5## is the fifth primitive root of unity). Homework Equations The Attempt at a Solution ##\zeta_5 + \zeta_5^2 = \cos(2\pi/5) + i\sin(2\pi/5) +...
  41. A

    Multiplying primitive roots of unity.

    Homework Statement Let ##ζ_3## and ##ζ_5## denote the 3rd and 5th primitive roots of unity respectively. I was wondering if I could write the product of these in the form ##ζ_n^k## for some n and k.Homework Equations The Attempt at a Solution We know that ##ζ_3## is a root of ##x^3=1##, and...
  42. L

    Unity Hypotenuse Model: Fig. WL & Fig. P

    Unity hypotenuse model. As a worldline Shown in Fig. WL. http://imageshack.us/photo/my-images/832/29j2.jpg/ Pythagorean treatment shown in Fig. P. http://imageshack.us/photo/my-images/827/8ggf.jpg/
  43. H

    Solving Roots of Unity with De Moivre's Theorem

    Homework Statement Use De Moivre's Theorem to solve for the roots of unity 1, ω, ω2 Hence show that the sum of these roots is zero Homework Equations r(cosθ + isinθ) r(cos(θ + 2n∏)+isin(θ+isin∏)) The Attempt at a Solution I know the first root,1, is 1(cos 0 + i sin 0) but have no clue about...
  44. Markus Hanke

    Eric Weinstein's "Geometric Unity" Hypothesis at Oxford

    Does anyone here have any information as to the contents of the presentation recently given by Eric Weinstein in Oxford on his "Geometric Unity" hypothesis ? http://www.simonyi.ox.ac.uk/simonyi-lectures/special-simonyi-lecture-2013-eric-weinstein I would be interested in getting some idea...
  45. Alesak

    What is function of period unity ?

    What is "function of period unity"? Hi, I'm reading an article that has a sentence saying "where P is a function of period unity.". Here. I've been looking for what does it mean but without any success. Does anyone know?
  46. A

    Value of parallel capacitance necessary to achieve a Power F. of unity

    Homework Statement The electrical model of an operating AC induction motor yields an impedance, Z, of 18.65+j15.106Ω . What value of parallel capacitance is necessary to achieve a power factor of unity if the operating frequency is 60Hz? Homework Equations V=IR w=2pif P=VI The...
  47. K

    Opamp - preceded by a unity buffer

    Homework Statement Hi, I'm trying to figure out the component values(Rf and C) for the circuit given. The circuit must be designed so that it has a cut-off frequency of 1khz and a low frequency magnitude gain of 1. I know how to do it if i ignore the unity buffer in front but I'm not sure how...
  48. V

    Why Does My Quad 741 Op Amp Not Function as Unity Gain Like My Single 741s?

    I have single 741 op amps running as unity gain amps and they work fine but when I tried to use a quad 741 op amp (LM348n) with the same config as the single 741 (short the inverting input to the Vout), the results are not correct. Can anyone provide a chip id and wiring config for a quad 741...
  49. T

    Solving for the roots of unity of a complex number

    Homework Statement Find both square roots of the following number: -15-8i Homework Equations De Moivre's thm: rn(cos(n\sigma) + i sin(n\sigma) The Attempt at a Solution So to use De Moivre's I have to find the modulus and the argument. actually in this question r =...
  50. Math Amateur

    MHB Principal Ideals - Need for a ring with identity or a unity

    On page 273 of Dummit and Foote the last sentence reads: (see attachment - page 273) "The notion of the greatest common divisor of two elements (if it exists) can be made precise in general rings." (my emphasis) Then, the first sentence on page 274 reads as follows: (see attachment - page...
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