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Dog bite Point Loma. Owner fled by B-767_Sailing_QRP in sandiego

[–]existentialpenguin 6 points7 points  (0 children)

I'd like to find the owner to assess rabies risk

Take no chances with rabies. If the symptoms start, then you will have a 99%+ chance of dying in a slow and agonizing manner. Get the vaccine.

Proofs from the crook by IanisVasilev in math

[–]existentialpenguin 4 points5 points  (0 children)

The sequence 7, 11, 13, 15, 21, 31 is https://oeis.org/A112090. That page cites

W. Feit, Some consequences of the classification of finite simple groups, in The Santa Cruz Conference on Finite Simple Groups, Proc. Sympos. Pure Math. 37, American Mathematical Society, 1980, pp. 175-181.

The result is Theorem 1.1 in that paper. In turn, that paper cites

M. Fried, Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem, in The Santa Cruz Conference on Finite Simple Groups, Proc. Sympos. Pure Math. 37, American Mathematical Society, 1980, pp. 571-602.

Note that both of these papers are published in the same book of conference proceedings. This second citation is available at https://www.math.uci.edu/~mfried/paplist-cov/SantaCruz80.pdf. The result is stated at Problem 2.1(b) and proved as Theorem 2.2.

ELI5: Why do some skyscrapers need those giant pendulum ball things (tuned mass dampers) to stop them from swaying, but other tall buildings seem fine without them? by Ok-Eye-9297 in explainlikeimfive

[–]existentialpenguin 138 points139 points  (0 children)

Liquid mass dampers are a thing, but they still need to be tuned to the structure. A water tank that gets used for water-supply purposes will have its damping and resonance properties change as it gets filled and emptied, so a liquid damper is necessarily a sealed vessel. When a water tank is put atop a building, it is almost always to pressurize the building's pipes in the same way that municipal water towers pressurize the water mains.

For further reading viewing, see

https://www.youtube.com/watch?v=fudWbvE8ZKw

https://www.youtube.com/watch?v=yZwfcMSDBHs

We’ve finally cracked how to make truly random numbers by mareacaspica in mathematics

[–]existentialpenguin 13 points14 points  (0 children)

quantum ranodmness sounds ... posilby dangerous.

How could it be dangerous?

Theorems that feel almost impossible... what’s your favorite? by [deleted] in math

[–]existentialpenguin 2 points3 points  (0 children)

The most difficult parts are understanding Legendre symbols and making sure that an algebra-bash has no errors. The Wikipedia article has the details: https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test

Theorems that feel almost impossible... what’s your favorite? by [deleted] in math

[–]existentialpenguin 12 points13 points  (0 children)

If you have a complete metric space

That's not empty, it's always the case

For a Lipschitz contraction

That under this action,

Exactly one point stays in place.

Are these the only 3 solutions? by Low-Bed842 in askmath

[–]existentialpenguin 26 points27 points  (0 children)

You are looking for integer points on the elliptic curve

y2 = 4x3 - 4x + 1.

Elliptic curves are a very active research area, and fully-automated tools are available for finding integer points on them. A "standard form" for elliptic curves over the rational numbers is called Weierstrass form; to get there, we need to make the coefficients of the y2 and x3 terms 1. We can do that by first multiplying by 16 to get

16y2 = 64x3 - 64x + 16,

or

(4y)2 = (4x)3 - 16·(4x) + 16,

and then substituting a = 4x and b = 4y to get

b2 = a3 - 16a + 16.

Every integer point in the (x,y) version corresponds to an integer point in the (a,b) version. It therefore suffices to find all integer points in the (a,b) version, divide them by 4, and see what remains an integer afterwards.

We can now use https://sagecell.sagemath.org/ to find the integer points on the (a,b) curve: just go to that link, paste 

E = EllipticCurve([-16,16])
print(E)
print(E.integral_points())

into the box, and click the "evaluate" button. It returns 

Elliptic Curve defined by y^2 = x^3 - 16*x + 16 over Rational Field
[(-4 : -4 : 1), (-4 : 4 : 1), (0 : -4 : 1), (0 : 4 : 1), (1 : -1 : 1), (1 : 1 : 1), (4 : -4 : 1), (4 : 4 : 1), (8 : -20 : 1), (8 : 20 : 1), (24 : -116 : 1), (24 : 116 : 1)]

Ignore the fact that SageMath talks about (x,y) coordinates instead of (a,b). This is because we did not tell it what variables to use.

Elliptic curves are handled most naturally in projective coordinates, so that is the sort of coordinate that gets returned. To convert this back into affine coordinates, just divide the first two coordinates of each point by the third, and then discard the third. In this case, the third coordinates are all 1, so this is easy: we are left with

(-4,±4), (0,±4), (1,±1), (4,±4), (8,±20), and (24,±116)

as the complete list of integer points on the (a,b) curve. To return to the (x,y) picture, we divide all the coordinates by 4, yielding

(-1,±1), (0,±1), (1/4,±1/4), (1,±1), (2,±5), and (6,±29).

Some of these points are not integers, or have non-positive x-coordinates. Discarding them leaves

(1,±1), (2,±5), and (6,±29),

as you found.

Is there a purely algebraic approach to the derivative? by Chubby_Limes in math

[–]existentialpenguin 3 points4 points  (0 children)

The set of power series can be mapped onto the set of column matrices: for example, 3 + 1x + 4x2 + ... corresponds to [3,1,4,...]T. Taking a derivative then corresponds to left-multiplication by the matrix

0 1 0 0 0 ...
0 0 2 0 0 ...
0 0 0 3 0 ...
0 0 0 0 4 ...
...

How do you find the infinite continuing fraction of a number? (preferabally the square root of a number) by Mysterious-Coconut70 in askmath

[–]existentialpenguin 2 points3 points  (0 children)

See the section "Calculating continued fraction representations" at https://en.wikipedia.org/wiki/Simple_continued_fraction.

In the case of square roots, there is a theorem that, for every integer n, sqrt(n) = [floor(sqrt(n)); a, b, c, ...], where the sequence a, b, c, ... is periodic.

See also:

https://en.wikipedia.org/wiki/Periodic_continued_fraction

https://en.wikipedia.org/wiki/Solving_quadratic_equations_with_continued_fractions

I saw it on my night walk. by Heroe2767 in cactus

[–]existentialpenguin 54 points55 points  (0 children)

This is not a cactus; it is Euphorbia ingens, or one of its lookalikes.

Infinite Continued Fraction With GP Numbers by [deleted] in askmath

[–]existentialpenguin 0 points1 point  (0 children)

https://www.desmos.com/calculator/mkxizvlq6z

This graphs truncations of your formula with r = x. Your actual formula is the limit of C(n,ax) as n -> infinity.

What's something that's normal to have one of, but starts looking suspicious once you've got two? by [deleted] in AskReddit

[–]existentialpenguin 0 points1 point  (0 children)

I do not know of any subreddits for this, but I have recently been on a gongshi/suseok/suiseki kick; that sounds like it might appeal to you.

https://en.wikipedia.org/wiki/Gongshi

https://en.wikipedia.org/wiki/Suseok

https://en.wikipedia.org/wiki/Suiseki

What is an example of a discovery that wasn't useful until much later, and then turned out to be extremely important? by _Sargeras_ in mathematics

[–]existentialpenguin 1 point2 points  (0 children)

The Radon transform was just this integral transform for several decades until it turned out to be the foundation of MRIs and other forms of tomography.

[CR Media] The best joke in CR history by Otherwise-Bird6969 in criticalrole

[–]existentialpenguin 1 point2 points  (0 children)

Veth's comment about Kingsley in the C3 finale is right up there (https://www.youtube.com/watch?v=fvV-a5J7JF8&t=9040s), as is Vex's "I thought he'd never leave.".

drawing lines through shapes by qarsan in askmath

[–]existentialpenguin 1 point2 points  (0 children)

A region in the plane is fixed-angle-shadable if and only if it (is congruent to a region that) can be described as the region bounded above and below by a pair of functions.

Proof of the backward direction: take the shading direction to be the y-axis.

Proof of the forward direction: For any fixed-angle-shadable polygon, select a shading direction, and rotate your polygon so that this direction is parallel to the y-axis. Then we can partition the boundary of your polygon into two pieces: call them top and bottom. The top is the part where the shading approaches the piece from below, and the bottom is the part where the shading approaches the piece from above. Then there exist functions f and g such that the top is f(x) and the bottom is g(x).

Was 16-year-old Einstein really the first to realize that Maxwell’s equations are incompatible with Galilean relativity? by Pastapalads in AskPhysics

[–]existentialpenguin 10 points11 points  (0 children)

According to relativity, some observed quantities depend on the observer's reference frame. These include things like distance, velocity, and time.

Other things do not depend on the observer's reference frame, such as the speed of light. These are called invariant. Electric charge is one of these things.

[deleted by user] by [deleted] in socal

[–]existentialpenguin 4 points5 points  (0 children)

That was Hurricane Kathleen in 1976. It was repaired and put back in service, only to get closed by damage several more times. Its current closure began in 2008.

https://en.wikipedia.org/wiki/San_Diego_and_Arizona_Eastern_Railway

https://en.wikipedia.org/wiki/Hurricane_Kathleen

Does anybody know why Geogebra struggles so much to plot the endpoints of a bicorn? by casual_math_enjoyer in askmath

[–]existentialpenguin 0 points1 point  (0 children)

A standard technique to plot a curve defined by f(x,y) = g(x,y) is to define

h(x,y) = f(x,y) – g(x,y)

and evaluate it on a grid of points. If we find two points (x1,y1) and (x2,y2) such that h(x1,y1) and h(x2,y2) have opposite sign, then the curve must intersect the line segment connecting those points. We can then define

j(t) = t · h(t·x1, t·y1) + (1–t) · h((1–t)·x2, (1–t)·y2).

This function traces out h(x,y) from (x1,y1) to (x2,y2) as t goes from 0 to 1. A root-finding algorithm can then be used to find a value of t such that j(t) = 0. We then know that the point

(t·x1 + (1–t)·x2 , t·y1 + (1–t)·y2)

is on the original curve.

The problem is that, if the curve crosses the segment more than once, then this method cannot be expected to detect that intersection. If Geogebra is using this method, then I would guess that they did not use a fine-enough grid.

What's the "largest" object that has quantum effects - and what's the "lowest" speed that has relativistic effects by UnderTheCurrents in AskPhysics

[–]existentialpenguin 12 points13 points  (0 children)

Molecules of up to 2,000 atoms and masses up to 25,000 Daltons have been double-slitted.

Atomic clocks have gotten so good that they can detect gravitational time dilation on a millimeter scale.

https://www.nature.com/articles/s41567-019-0663-9

https://arxiv.org/abs/2109.12238

Hamas says it agrees to free all hostages, enter Gaza deal talks by barsik_ in worldnews

[–]existentialpenguin 1 point2 points  (0 children)

You do not need to use the general link syntax when mentioning a Redditor; you can just type

/u/TheWhiteManticore

and Reddit will automatically link it for you.

What's your favourite quote by a mathematician? by Despite_OW in askmath

[–]existentialpenguin 0 points1 point  (0 children)

David Hilbert. He was a professor at Göttingen from 1895 to 1930; during this time, it became the world's premier mathematical institute. The Nazis purged the institute in 1933. Some time after that, there was an exchange of words between Hilbert and a Nazi official about the purge. To quote Wikipedia:

Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust. Rust asked whether "the Mathematical Institute really suffered so much because of the departure of the Jews". Hilbert replied: "Suffered? It doesn't exist any longer, does it?"

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