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Even about ~5 years back this was a popular notion that particles were being made from waves or light with fields whose excitations manifest as particles. But modern physics has changed the viewpoint, as far as I know, electrons are fundamental particles, so they aren’t made of anything. They’re excitations of the electron field (not to be confused with the electric field).
If had to explain, in an atom the electron field gets the localized shape it has because there are also nearby excitations in the quark field (in the nucleus). The quarks are charged and interact with the electromagnetic field, which also interacts with the electron field.
So you basically have three fields at play here: quark field, electron field and electromagnetic field. They all interact together such that they each get a particular "shape".
What we mean by "interact" is that mathematically the value of one field depends on the value of another field.
In Quantum Mechanics (actually Quantum Field Theory) the "value" of a field is something a bit more abstract than e.g. a single scalar number or vector quantity - instead the "value" is called a "state". I can't really explain what a "state" is in QFT so easily without the Bra-ket, except that it is indeed the mathematical "object" that fully describes what state or configuration the field/particle is in.
lol, i think you should follow my posts, i'm not doing a promo but you won't miss the bounties further. It's up to you of course if you want to or not.
wait this was way too quick 😂
was it so easy?
anyway, looks like we got our winner this time too!
Congo to @SimpleStacker 🎉 :)
no one tried it still? :/
is it too hard?
Let me drop some useful formula:
Given:
m=0.2\ \mathrm{kg}, h=10\ \mathrm{m}, b=0.4\ \mathrm{kg/s}, g=9.8\ \mathrm{m/s^2}k=\frac{b}{m}=\frac{0.4}{0.2}=2\ \text{s}^{-1}.Velocity:
v(t)=\frac{g}{k}\big(1-e^{-kt}\big).Position (distance fallen after time (t)):
y(t)=\int_0^t v(t')\ dt'=\frac{g}{k}t+\frac{g}{k^2}\big(e^{-kt}-1\big).= \frac{g}{k}t+\frac{g}{k^2}\big(e^{-kt}-1\big)=h.now just plug in numbers...
it won't be proven until apple admits it themselves lol
but no one's stopping us from cooking up conspiracy theories in the meantime :)
Yes, must be but not always. Most apple product edges fit this criteria, except some like the latest Apple watches which are a squircle and not a quintic superellipse.
Parametric equations define curves and surfaces through adjustable parameters, was used in architectural designs such as the Beijing National Stadium's steel web structure. It's a good tool to make graphic art too.
Even more fascinatingly Felix Candela's architectural shapes were primarily based on mathematical models of surfaces from Euclidean geometry, with a special focus on hyperbolic paraboloids, often called "hypars."
Candela became world famous for pioneering thin-shell concrete structures, particularly those with hyperbolic paraboloid shapes that are remarkably thin (often only 1.5 inches thick) but structurally very strong - he was a revolution in architecture.
Furthermore the 4 fathers of architecture:
- Le Corbusier
- Mies van der Rohe
- Frank Lloyd Wright, and
- Louis Kahn
Were GODS because they delved mathematics with engineering:
- Le Corbusier famously used the "Modulor" system, a scale of proportions based on the human body and the golden ratio, combining rectangles, squares, and circles to achieve harmonious, human-centered dimensions.
His buildings, like Villa Savoye, feature geometric rigor with golden section rectangles, circle arcs, and diagonal grids - chef's kiss.
- Frank Lloyd Wright embraced organic architecture, drawing mathematical inspiration from natural forms like spirals and helicoids seen in snail shells. His designs incorporate curves and geometric patterns based on the golden ratio and fractal-like repetitions that integrate buildings with their environment. The Guggenheim Museum in New York, with its iconic spiraling ramp, is a prime example.
- Louis Kahn is known for his use of monumental geometric forms, especially cubes, cylinders, and circles arranged with careful attention to spatial order and light. His works often feature cubes rotated relative to one another and intersecting geometric volumes, exemplified in buildings like the Yale University Art Gallery and the National Assembly in Bangladesh (Jatiya Sangsad Bhavan) (very famous to my parents).
Haha, that's how you make aesthetics (and abominables too)
btw, superellipses are part of topology, a topic that @beyond_turbulence always keeps blabbing supposedly nonsense and making parodies out of, lol
you can now pay for things on SN with mixed assets, e.g. if your post costs 100 sats and you have 20 CCs and 50 reward sats you'll only need to pay a 30 sat invoice noncustodially
yeeeee! that's a feature I have been hoping for since I joined SN.
Also, I think this issue can be closed now?
you still can, and I'll still give sats if you do it other than the 3 ways already done :)
and this is not the last one, I'll be posting plenty....
I am designating @Scroogey as the winner for this bounty with a -200 sats (for admitting to use a solver lol, although that does not give away the answer).
He showed the right steps and right equations (check second pinned comment)!
Here is another simpler walkthrough by me though (simple factorization)
or using Ferrari's method for quartic polynomials:
that's okay, but the rational root test link shows you solved the equation using a solver which is not okay, had you not posted the link and only written "rational root test", I might not have figured it out, but since you did, it puts a wrong impression
it's okay to use a solver once you understand the method, but citing is not always necessary! (another lesson I learnt the hard way)
but another 200 sats for being honest and using formulas the correct way!