# What is Square: Definition and 1000 Discussions

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or 100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted

{\displaystyle \square }
ABCD.

View More On Wikipedia.org
1. ### Find sum of all odd square numbers

There is a mistake on this textbook (The mistake is pretty obvious) but hey I hope I did not miss something... ought to be ##40425 - 19600##
2. ### I In which sense(s) do square integrable functions go to zero at infinity?

In which sense(s) do square integrable functions go to zero at infinity? Of course, they cannot go to zero at infinity in the sense of point evaluation, because point evaluation is not the appropriate concept for square integrable functions. There was a recent discussion in the Quantum Physics...
3. ### Square of orthogonal matrix vanishes

I found a the answer in a script from a couple years ago. It says the kinetic energy is $$T = \frac{1}{2} m (\dot{\vec{x}}^\prime)^2 = \frac{1}{2} m \left[ \dot{\vec{x}} + \vec{\omega} \times (\vec{a} + \vec{x}) \right]^2$$ However, it doesn't show the rotation matrix ##R##. This would imply...
4. ### B Does the inverse square law equalize gravity at different spots?

Inverse square law would reduce the gravity from the parts of Earth that are farthest from our feet. It'll also reduce the gravity from Earth's center by a lesser amount, but would that be lesser enough so the gravity 20 kilometers under our feet is stronger than the core's gravity or even the...
5. J

### I Noise Proportional to Square Root of Illumination: Need Formula Help

Many people have said that the noise that affects laser light is proportional to the square root of the illumination. But I can't find the formula. Can anyone help?
6. ### Solving Equations: Does Squaring Make False True?

Does this mean for x=1 , ##2(1)-1= -\sqrt{2-1}## is false. x=1 is not a solution. But as we square the above equation , ##(2(1)-1)^2=(-\sqrt{2-1})^2## , false equation becomes true. So now x=1 is solution to the new equation ? (Here is the paragraph attached) from book James Stewart.
7. ### Crush Strength Of Donut Shaped 1.5 x 1.5 Square Tubing

Hi All, I am working on a project where I am using a donut shaped 1.5 x 1.5 square tubing. It is mild steel and I am assuming it has a 16 gauge wall thickness. I bought this already fabricated and don't know for sure (its possible its 14 gauge). The outside dimension of the donut is 89.5". I am...
8. ### B Solve for ##c## for this rotated square

I'm getting a quartic in ##c##, is there a way around that...perhaps something elegant I'm missing?
9. ### A particle in an infinite square well

What I am lost about is b, rather the rest of B. I am not sure what it means by probability density and a stationary state.
10. ### Thermal expansion of square from temperature increase of 50K

For this problem, The solution is, I understand their logic for their equation, but when I was trying to solve this problem, I came up with a different expression: ##\Delta A = \Delta L_x\Delta L_y## ##\Delta L_x =\Delta L_y = \Delta L## since this is a square. ##\Delta A = \Delta L^2##...

20. ### B Proof of inverse square law for gravitation?

Newton arrived at "there is a force that drives a planet around the star by examining kepler's laws but how did he arrive to inverse square law by kepler's third law (##T^2=\frac {4\pi r^3}{GM}##)? Thank you.
21. ### Rationalizing this fraction involving square roots

I can do the question using brute force. First I multiply both the numerator and denominator by ##\sqrt{5} + \sqrt{3} - \sqrt{2}## then I simplify everything and rationalize again until no more square root in the denominator. I want to ask if there is a trick to reduce the monstrous calculation...
22. ### Moment of inertia of a uniform square plate

I placed my Oxy coordinate system at the center of the square, the ##x##-axis pointing rightwards and the ##y##-axis pointing upwards. I divided the square into thin vertical strips, each of height ##h=2(\frac{L}{\sqrt{2}}-x)##, base ##dx## and mass ##dm=\sigma h...
23. ### Quantum mechanics - finite square well

In a) I get that T should be largest where V_0 is least wide, because when V_0 is infinitely wide the particle would be fully reflected. But I don't get how height in b) and energy levels height in c) correlates to T and R. Is it because of their k? I get the opposite answer from the correct...
24. ### Quantum mechanics - infinite square well problem

I have solved c), but don’t know how to solve the integral in d. It looks like an integral to get c_n (photo below), but I still can’t figure out what to make of c) in the integral of d). I also thought maybe you can rewrite c) into an initial wave function (photo below) with A,x,a but don’t...
25. ### No integer whose digits add up to ## 15 ## can be a square or a cube

Proof: Let ## a ## be any integer. Then ## a\equiv 0, 1, 2, 3, 4, 5, 6, 7 ##, or ## 8\pmod {9} ##. This means ## a^{2}\equiv 0, 1, 4, 9, 7, 7, 0, 4 ##, or ## 1\pmod {9} ## and ## a^{3}\equiv 0, 1, 8, 0, 1, 8, 0, 1 ##, or ## 8\pmod {9} ##. Thus ## a^{2}\equiv 0, 1, 4 ##, or ## 7\pmod {9} ## and...
26. ### Bragg angle with an inclined plane through a square lattice

Suppose a square lattice. The planes are such as the image below: I light wave incides perpendicular to the square lattice. The first maximum occurs for bragg angle (angle with the plane (griding angle) as ##\theta_B = 30°## (blue/green), green/blue in the figure). The angle that the...
27. ### Quick math question with square roots

If I wanted to remove c from the square root, ## r ={ \sqrt{c^2} + {x} } ## would this be correct ## r = \sqrt { {c} + {x} } {c} ## ?
28. ### If ## n>1 ##, show that ## n ## is never a perfect square

Proof: Let ## n>1 ## be an integer. By definition of factorial, ## n!=n\times (n-1)\times \dotsb \times 1 ##. Now we consider two cases. Case #1: Suppose ## n ## is odd. Then ## n=2k+1 ## for ## k\geq 1 ##. Note that ## n!=(2k+1)!=(2k+1)\times (2k+1-1)\times \dotsb \times 1\implies (2k+1)\times...
29. ### MHB True or False Question about Square Matrices

[MHB thread moved to the PF schoolwork forums by a PF Mentor] For every square matrix A, C=A(A^t)+(A^t)A is symmetric.
30. ### Find the area of the shaded region in the inscribed circle on square

Find the solution here; Find my approach below; In my working i have; ##A_{minor sector}##=##\frac {128.1^0}{360^0}×π×5×5=27.947cm^2## ##A_{triangle}##=##\frac {1}{2}####×5×5×sin 128.1^0=9.8366cm^2## ##A_3##=##\frac {90^0}{360^0}####×π×10×10##=##78.53cm^2## ##A_{major...
31. ### Criterion for a positive integer a>1 to be a square

Proof: Suppose a positive integer ## a>1 ## is a square. Then we have ## a=b^2 ## for some ## b\in\mathbb{Z} ##, where ## b=p_{1}^{n_{1}} p_{2}^{n_{2}} \dotsb p_{r}^{n_{r}} ## such that each ## n_{i} ## is a positive integer and ## p_{i}'s ## are prime for ## i=1,2,3,...,r ## with ##...
32. ### B Does this kind of square matrix exist?

I had a homework question that gives A as an arbitrary matrix. Then the question states that A^2=A Now I manipulate the equation to give this A^2-A=0. -->A(A-I)= 0 So A can be I or 0 Are there any other values A can take?
33. ### The only prime p for which 3p+1 is a perfect square is p=5?

Proof: Suppose that p is a prime and 3p+1=n^2 for some n##\in\mathbb{Z}##. Then we have 3p+1=n^2 3p=n^2-1 3p=(n+1)(n-1). Since n+1>3 for ##\forall...
34. ### B Derivative of Square Root of x at 0

When you use the power rule to differentiate the square root, the result is 1/2(sqrt. x) which is undefined at 0. But, when you use the definition of the definition of the derivative to calculate it, the result is infinity. What causes this difference between these two methods?
35. ### Renormalization Group:NiemeijerVan Leeuwen Method-Ising Square Lattice

Hello, I have to solve this problem. I will apply the Niemeijer Van Leeuwen method once I have the probability distribution proper to the renormalization group ,P(s,s'). For example, in the case of a triangular lattice, this distribution is: where I is the block index. However, it is very...
36. ### I Infinite Square Well with an Oscillating Wall (Klein-Gordon Equation)

I am trying to numerically solve (with Mathematica) a relativistic version of infinite square well with an oscillating wall using Klein-Gordon equation. Firstly, I transform my spatial coordinate ## x \to y = \frac{x}{L[t]} ## to make the wall look static (this transformation is used a lot in...
37. ### Inverse square law of gravitation and force between two spheres

I recently encountered this problem on a test where the solution for the above problem was given as follows: $$F= \frac{Gm_1m_2} {r^2}$$ (1) but $$m=\frac{4}{3}\pi R^3$$ substituting in equation (1) $$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2}$$ where r=radii of the two spheres m=mass...
38. ### Demodulation of modulating square wave

Hi all There is RF signal in frequency range of 240 MHz to 500 MHz which has been amplitude modulated by 155 Hz square wave signal. The problem is to recover 155 Hz signal while exact RF Carrier frequency is unknown (240 MHz to 500 MHz). Is there any ready made COTs solution available for such...
39. ### Fresnel diffraction from square: on axis intensity

I'd appreciate if someone could check whether my work is correct. The ##x##-##y## symmetry of the aperture separates the Fresnel integral:\begin{align*} a_p \propto \int_{-a/2}^{a/2} \mathrm{exp}\left(\frac{ikx^2}{2R} \right) dx \int_{-a/2}^{a/2} \mathrm{exp}\left(\frac{iky^2}{2R} \right) dy...
40. ### B Square Root of an Odd Powered Integer is Always Irrational?

Is it always true that the square root of an odd powered integer will always be irrational?
41. ### Show that square root of 3 is an irrational number

##\sqrt{3}## is irrational. The negation of the statement is that ##\sqrt{3}## is rational. ##\sqrt{3}## is rational if there exist nonzero integers ##a## and ##b## such that ##\frac{a}{b}=\sqrt 3##. The fundamental theorem of arithmetic states that every integer is representable uniquely as a...
42. ### MHB What is the area of square ABCD with OQ = OF = 6?

Find area of square ABCD if OQ=OF=6.
43. ### Find next perfect square -- Not working in python

def find_next_square(sq): # Return the next square if sq is a square, -1 otherwise sq2=(sq**1/2) xyz=isinstance(sq2, int) if (xyz==True): print("Is perfect square") nextsq=sq+1 print("Next perfect square=",nextsq**2) else: print("Not...
44. ### Find next perfect square not working in python

def find_next_square(sq): # Return the next square if sq is a square, -1 otherwise sq2=(sq**1/2) xyz=isinstance(sq2, int) if (xyz==True): print("Is perfect square") nextsq=sq+1 print("Next perfect square=",nextsq**2) else: print("Not perfect...

49. ### I Encircled energy for different aperture shapes (circle, triangle, square)

Hi all, I have a system whereby, there are different aperture shapes which are: circle, triangle, square e.t.c. this apertures are all 300um in diameter. I will like to know if the encircled energy calculated for the different apertures after diffraction will be different due to different...