Formula Definition and 1000 Threads

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.
The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula(often referred to as a well-formed formula) is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius:




V
=


4
3


π

r

3




{\displaystyle V={\frac {4}{3}}\pi r^{3}}
.Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic, analytical or in closed form.In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O−3 denotes an ozone molecule consisting of three oxygen atoms and a net negative charge.
In a general context, formulas are a manifestation of mathematical model to real world phenomena, and as such can be used to provide solution (or approximated solution) to real world problems, with some being more general than others. For example, the formula

F = mais an expression of Newton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.
Expressions are distinct from formulas in that they cannot contain an equals sign (=). Expressions can be liken to phrases the same way formulas can be liken to grammatical sentences.

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  1. F

    Is the Rydberg formula true for electron absorption only?

    Since we know that when an electron goes from the ground state (hydrogen) n=1 to n=3 for example, we have ΔE = E3 - E1 by manipulating the equation we get Rydberg's formula 1/λ= R (1/ni2 - 1/nf2) (where R is Rydberg's constant) My question here, if the electron goes from higher energy state...
  2. F

    Does this formula exist? (ν' = En/hc)

    ν' = En/hc ? ν' is the wavelenght's number (in electromagnatique radiation) where ν' = 1/λ if so, how do we get it ?
  3. M

    Wave equation in inhomogeneous media -- Question about the formula

    https://i.hizliresim.com/ZO0bvG.jpg I don't understand that where ε0/ε is coming from? Can you explain this?
  4. M

    MHB Calculate density using convolution formula

    Hey! :o Let $X_1, X_2, X_3$ be i.i.d. with $X_1 \sim U[0, 1]$. I want to determine the density of $S=X_1+X_2+X_3$ using the convolution formula. I have done the following: Since $X_1, X_2, X_3$ are i.i.d. we have that they are independent identically distributed random variables. Since $X_1...
  5. J

    I Understanding Equation (2.34) in Heald and Marion: A Step-by-Step Derivation

    Would someone explain the last step in eq.(2.34) in Heald and Marion? Much thanks ahead.
  6. Z

    Interior and Exterior Angle of a Polygon: Formula not working

    Homework Statement How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle? Homework Equations Interior angle of a polygon: ((n-2) * 180)/n Exterior angle of a polygon: (360)/n The Attempt at a Solution ((n-2) * 180)/n = 8 *...
  7. M

    How can the recurrence formula for a sequence be found?

    Homework Statement Find a recurrence formula for the sequence (ai) = 1, sqrt3, sqrt(1+sqrt3), sqrt(1+sqrt(1+sqrt2)) in terms of i and ai Homework EquationsThe Attempt at a Solution no idea where to start, this is a bonus question, and I have learned how to solve these type of problems
  8. S

    What Must Remain Constant for W = pΔV to Apply?

    Homework Statement The work done W by an expanding gas is calculated using W = pΔV. What must remain constant for this equation to be used? a. The pressure of the expanding gas b. The pressure of the surroundings c. The temperature of the expanding gas d. The temperature of the surroundings e...
  9. HenryM

    Deriving the formula for tidal generating force TGF

    i have been asked to show that the TGF acting on a 1kg mass, on the surface of the Moon is equal to: TGF = 2g.e^2.(a/r^3) Where; g = 9.81 e = radius of the Earth a = radius of the Moon r = distance between the centres of the Earth and Moon.
  10. ferrariistheking

    Formula 1 Racing: Evolution or Standardization?

    Anybody interested in Formula 1 racing?
  11. C

    What is the correct formula for refraction at an interface between two media?

    Hi! I have a problem understanding what happens when a plane electromagnetic wave hits a surface consisting of two medias of different optical density. My old school litterature tells me two formulas which I really don't understand where they come from. The same teacher starts by telling me...
  12. K

    A Question about Wall crossing formula

    I am looking at the wall-crossing formula for N=2 D=4 supersymmetry The Donaldson-Thomas "invariant" is supposedly given by \Omega = -\frac{1}{2} Tr (-1)^{(2J_3)} (2J_3)^2 + I don't understand how to use this formula. (By the way, the normalization is probably not the same for everyone so you...
  13. L

    MHB Formula for changing a plane intersection angle

    Hello, This is a bit more complex than my previous post, but I don't think it qualifies for university level difficulty. Please move this to the appropriate forum if my assessment is not correct. I have 4 vectors in three space where each vector has its tail at the same point (point B). id...
  14. L

    MHB Formula to extend a line in 3d (opposite of midpoint formula)

    Hello, I have some simple 3d data like, point 1: x1 = 5.8573375, y1 = -4.17885, z1 = 2.338175 point 2: x2 = -3.26132, y2 = 1.28276, z2 = 0.931583 I need to be able to extend the line from point 1 through point 2 to some additional distance. There are a few posts on stackexchange, but they...
  15. D

    Derive Formula for Velocity of Object Approaching Earth

    Homework Statement A particle of mass m is dropped from a height h, which is not necessarily small compared with the radius of the earth. Show that if air resistance is neglected, the speed of the particle when it reaches the surface of the Earth is given by ##\sqrt {2gh}## ##\sqrt {\frac {R_E}...
  16. M

    MHB Unique Area of Triangle Formula

    I think the following formula is so cool.
  17. I

    A Recurrence Formula for 3,5,13,27,55,...

    What is the recurrence formula for the sequence [3,5,13,27,55,...] Thank you for any help.
  18. S

    I Understanding Kunneth Formula and Tensor Product in r-Forms

    Hello! Kunneth fromula states that for 3 manifolds such that ##M=M_1 \times M_2## we have ##H^r(M)=\oplus_{p+q=r}[H^p(M_1)\otimes H^q(M_2)]##. Can someone explain to me how does the tensor product acts here? I am a bit confused of the fact that we work with r-forms, which are by construction...
  19. O

    Which formula to use to find the pH of a solution?

    Hello, I just had my first exam yesterday, and I'm always tripped with this question that combines neutralization with buffer solution. The task is to find the pH. I did try to understand the general concept behind it. From my understanding, if CH3COOH reacts with NAOH and the acid has a higher...
  20. J

    I How to determine if an asteroid will burn up or hit Earth?

    I want to make a interactive simulation that shows whether or not an asteroid will hit the surface of the Earth. It would have 2 sliders for you to control the speed and mass of the asteroid. The simulation will output "yes" or "no" if the asteroid hits the surface. Is there a mathematical...
  21. M

    Not exactly a homework issue - just trying to find a formula

    Alright, first I should probably let you all know that this is very simple physics, so I'm just looking for a quick answer. 1. Homework Statement I'm trying to find a simple way to calculate the average velocity of an object where we know the average velocity during a number of segments of...
  22. Y

    Can someone figure out the formula of this sequence?

    I needed help figuring out the formula for a sequence with these conditions: 1. The first term is 1. 2. All terms are positive integers. 3. 3 times each term (3*a_n) must be greater than the sum of that term and all the terms before it, but no more than 3 greater. Operators like ceil() and...
  23. MathematicalPhysicist

    Equilibrium Statistics -- Euler summation formula

    Homework Statement In the calculation in high temperatures of ##Z_{rot} = (\sum_{j=0}^\infty (2j+1)\exp{j(j+1)\theta_{rot}/T})^N##; they use Euler summation formula: $$\sum_{n=0}^\infty f(n) = \int_0^\infty f(x)dx+\frac{1}{2}f(0)-\frac{1}{12}f'(0)+\frac{1}{720}f^{(3)}(0)+\ldots$$ for ##f(x) =...
  24. A

    Finding the Formula for Speed and Distance on an Icy Hill

    Homework Statement Maxine (mass m) slides down an icy slope then along a flat surface before coming to a stop. The slope has angle θ and height h. a. Derive a formula for speed at the bottom of the hill in terms of the angle of the hill θ, the height from which she starts h, and the...
  25. L

    Finding the correct formula for the speed of waves in shallow water

    Question: The speed of waves in shallow water depends only on the acceleration due to gravity (g) and the water depth (h). Which of the following formulas describes the speed of the wave? a) (1/2)gh^2 b) gh c) h/g d)(gh)^(1/2) Attempt: Change in V = at t= ΔV/a Δx=vt+(1/2)at2 Δx =...
  26. S

    MHB Proving a formula ∀x:x∈A∧|x−1|<a⟹x=1

    Given the set {1,2},prove that there axists an a>0 such that: \forall x:x\in A \wedge |x-1|<a\Longrightarrow x=1
  27. yecko

    Specific heat at constant pressure formula help

    Homework Statement https://i.imgur.com/f2vSXtq.png Homework Equations https://i.imgur.com/Kjy1Tzh.png The Attempt at a Solution In this question, the pressure is different at different point, in other words it is not constant throughout the system. Why the solution use c(p) (or "enthalpy" h...
  28. A

    I Help with an expectation value formula

    Imagine a particle in an equally weighted superposition of being located in three distant regions P, Q, and R, and imagine you stand in region P with a measuring device. The probability of finding the particle there is 1/3. Now imagine a large number N of particles prepared in that same state...
  29. S

    B Tips on writing a formula in rigorous way

    Dear, I am writing a report of a tool I have developed where there is a chapter with all the formulas included in the tool. I have a formula like the following: P(l,1)=\sum_k PF(k,l) but P(l,1) contains the sum of all the positive PFs, while P(l,2) contains the sum of all the negative PFs. Is...
  30. R

    Solving Voltage Ripple Formula: Get the Right Answer!

    Hi lads, Working through my HND course books and I have come across a formula that I cannot get to give me the same answer as the book. Nor can some of my engineering student friends. Values are: F=50 C=500^-6 Rl = 100 Vc=31.03 The formula is =(1/(2FsCRl))*(Vc-(Vr/2)) Inputting the values...
  31. S

    Lenz' Law - request for formula (for 2 given cases)

    Homework Statement Assume a uniform hollow cylindrical copper tube with the following parameters: Inner radius = R0 Outer Radius = R1 Length = L1 (Length > Outer Radius) Mass = M1 Now assume a cylindrical permanent magnet with the parameters: Length = L0 (L0 < L1) Mass = M0 Magnetic...
  32. M

    Dimensional formula of distances in certain formulas

    Homework Statement Dimensional formula for 'the square of the distance between two bodies' in universal gravitation and 'distance from the axis squared' in moment of inertia. Is L^2 is the dimensional formula for both the distances in the above two cases? Homework Equations F=Gm1m2/d^2; moment...
  33. S

    Formula confusion for magnetic field inside capacitor

    Homework Statement Uploaded question(the formula in c part) And can you tell me in which all cases that formula is used. Homework Equations Just want to know where the formula in c part has come from. The Attempt at a Solution Sum of magnetic fields due to circular plates calculated and added...
  34. B

    A Intuition on integral term in D'Alembert's formula

    If $$\phi(t,x)$$ is a solution to the one dimensional wave equation and if the initial conditions $$\phi(0,x) , \phi_t(0,x)$$ are given, D'Alembert's Formula gives $$\phi(t,x)= \frac 12[ \phi(0,x-ct)+ \phi(0,x+ct) ]+ \frac1{2c} \int_{x-ct}^{x+ct} \phi_t(0,y)dy . \tag{1}$$ which is...
  35. B

    Formula of potential energy of a nucleus

    Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$
  36. J

    I Finding formula for nth term in sequence

    ##\displaystyle f_{n} = ((\sum_{k= \lfloor{\frac{n}{2}}\rfloor}^{n-1}f_{k}) mod 1) + 0.1## ##\displaystyle f_{1} = 0## I really would like to know where to begin for finding a formula for the nth term, I wrote out a bunch of the terms and couldn't really eyeball a pattern of any sort. I noticed...
  37. T

    I Relativistic Aberration Formula & Lorentz Transformation

    Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...
  38. B

    A Understanding the LSZ Reduction Formula in Quantum Field Theory

    My background is QM as done in Griffiths( So yes I have a background of operators, observables and scattering matrix), Classical fields as done in Goldstein and Particle physics as in Griffiths. Griffiths actually works out Feynman rules for QED and QCD. I've started QFT with Peskin and...
  39. B

    I Derivation of the atomic nucleus formula

    Does anyone know the heuristic derivation of this formula? $$R=r_{0} \cdot A^{\frac{1}{3}}$$ with ##R## the atomic nucleus, ##r_0## the radius of a nucleon (proton or neutron) and ##A## the number of nucleons. I know that there is a sperimental derivation, but I would find a theoretic/heuristic...
  40. D

    I with the formula for this marble falling from a platform

    A marble is released at 22.5 meters per second from a 70 meter tall platform. When will the marble strike the ground if the equation for the platforms height is 2.3[t][/2]+ (-)6.5t+70?
  41. W

    Complex Numbers: Euler's formula problem

    Homework Statement Homework EquationsThe Attempt at a Solution I attempted to use the formula zj = xj + iyj to substitute both z's. Further simplification gave me (x1 + x2)cosθ + (y2 - y1)sinθ or, Re(z2 + z1)cosθ + Im(z2 - z1)sinθ. Is this a valid answer? Or are there any other identities...
  42. P

    The formula for Thick-Edge Orifice

    Hi all, I have some problem in my research about the thick-edge orifice formula. I can't find the influence of orifice length to the discharge. I have found an online calculator for it but I can't find the formula derivation. Anybody can help me? Anybody have recommended literature? The...
  43. D

    B The Square of the Sum Formula and real world scenarios

    I'm starting with my self studying of math with Algebra I. The text I'm using is Gelfand and Shen's Algebra. I'm at the point where it talks about the Formula for the Square of the Sum, The Square of the Distance Formula, and The Difference of Squares Formula. In going over this, I understand...
  44. EEristavi

    An Error Formula for Linearization (involving second Derivative)

    Homework Statement In textbook i was given formula to calculate error. I know that: E(t) = f(t)- L(x) = f(t) - f(a)- f'(a)(t- a) [L(x) is linear approximation]; [Lets call this Formula 1] I understand that, but that I have formula: E(x) = f''(s)/2 * (x-a)^2 [lets call this Formula 2] Here...
  45. H

    I Can Emission Theory Produce Doppler-Shift Formula?

    Emission theories propose that the velocity of light depends on the velocity of the light source. But the ordinary Doppler effect assumes the velocity of light remains as ##c## with respect to the ether medium, even when the light source is moving at speed ##v## with respect to the ether. They...
  46. alex4lp

    A Solve Bending of Light Formula Problem

    Good morning everybody. I have a problem with this wikipedia passage https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Bending_of_light_by_gravity 'cause it says "Expanding in powers of rs/r, the leading order term in this formula gives the approximate angular deflection δφ for a massless...
  47. P

    Significant Figures with Kinetic Energy Formula?

    Homework Statement An object of mass m = 2.3±0.1 kg is moving at a speed of v = 1.25±0.03 m/s. Calculate the kinetic energy (K = 1 /2mv2 ) of the object. What is the uncertainty in K? I am not exactly sure if I used the error equation correctly when I start using Δ(v2). Could someone verify my...
  48. noir1993

    A Dyson's Formula from Tong's lecture notes

    I am studying quantum field theory from [David Tong's lecture notes][1] and I am stuck at a particular place. In Page 52., under the heading *3.1.1 Dyson's Formula*, Tong introduces an unitary operator U(t, t_0) = T \exp(-i\int_{t_0}^{t}H_I(t') dt') He then introduces the usual definition of...
  49. S

    I Where does the formula I = -e/T comes from?

    Yeah, where does it comes from?
  50. P

    I Help with formula to calculate the precession rate change

    First time caller, I'm a newb so go easy on me. So I was trying to work through a calculation to figure out the precession rate variation in terms of the Precession of the Equinox. I came across the following formula from...
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