Difference between revisions of "Sandbox"
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* [[Exotic math]] | * [[Exotic math]] | ||
* [[Pages containing math]] | * [[Pages containing math]] | ||
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| + | === For real d orbitals ''ℓ'' = 2 === | ||
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| + | * Source: https://en.m.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics | ||
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| + | <math display="block"> \begin{align} | ||
| + | Y_{2,-2} & = d_{xy} = i \sqrt{\frac{1}{2}} \left( Y_2^{- 2} - Y_2^2\right) = \frac{1}{2} \sqrt{\frac{15}{\pi}} \cdot \frac{x y}{r^2} = \frac{1}{4} \sqrt{\frac{15}{\pi}} \sin^{2}\theta \sin(2\varphi) \\ | ||
| + | Y_{2,-1} & = d_{yz} = i \sqrt{\frac{1}{2}} \left( Y_2^{- 1} + Y_2^1 \right) = \frac{1}{2} \sqrt{\frac{15}{\pi}} \cdot \frac{y \cdot z}{r^2} = \frac{1}{4} \sqrt{\frac{15}{\pi}} \sin(2 \theta) \sin \varphi \\ | ||
| + | Y_{2,0} & = d_{z^2} = Y_2^0 = \frac{1}{4} \sqrt{\frac{5}{\pi}} \cdot \frac{3z^2 - r^2}{r^2} = \frac{1}{4} \sqrt{\frac{5}{\pi}} (3\cos^{2}\theta -1)\\ | ||
| + | Y_{2,1} & = d_{xz} = \sqrt{\frac{1}{2}} \left( Y_2^{- 1} - Y_2^1 \right) = \frac{1}{2} \sqrt{\frac{15}{\pi}} \cdot \frac{x \cdot z}{r^2} = \frac{1}{4} \sqrt{\frac{15}{\pi}} \sin(2 \theta) \cos \varphi\\ | ||
| + | Y_{2,2} & = d_{x^2-y^2} = \sqrt{\frac{1}{2}} \left( Y_2^{- 2} + Y_2^2 \right) = \frac{1}{4} \sqrt{\frac{15}{\pi}} \cdot \frac{x^2 - y^2 }{r^2} = \frac{1}{4} \sqrt{\frac{15}{\pi}} \sin^{2}\theta \cos(2\varphi) | ||
| + | \end{align}</math> | ||
= For New Main Page = | = For New Main Page = | ||
Revision as of 01:47, 9 February 2025
Contents
[hide]Safe spaces for reprap wiki pre-writes – due to the logout time there being waaaaay to short
Testing image layouts
info-box-template snatched from Wikidata
Wanted: Better layout for main-page. => learn from Wikidata.
- wikidata main page frame
- wikitata MP without pics
- How are those placed side by side?
- How are the images made to scale with browser-window-size?
Test math
ϕ=∫π−πsin(x)dx
For real d orbitals ℓ = 2
Y2,−2=dxy=i√12(Y−22−Y22)=12√15π⋅xyr2=14√15πsin2θsin(2φ)Y2,−1=dyz=i√12(Y−12+Y12)=12√15π⋅y⋅zr2=14√15πsin(2θ)sinφY2,0=dz2=Y02=14√5π⋅3z2−r2r2=14√5π(3cos2θ−1)Y2,1=dxz=√12(Y−12−Y12)=12√15π⋅x⋅zr2=14√15πsin(2θ)cosφY2,2=dx2−y2=√12(Y−22+Y22)=14√15π⋅x2−y2r2=14√15πsin2θcos(2φ)
For New Main Page
Don't fall pray to the prime distractions.
Whats new on this wiki?
Where we're at and where we're headed to.
Current state
Template:Cutting edge
(wiki-TODO: make cutting edge info-box with: sketch of structural DNA hinge mechanism & atom placement demo)
(wiki-TODO: add infobox with structural DNA hinge left and atom placement example right – plus contxt images?)
Far term target
 A personal desktop gem-gum factory fabblet with dynamically deployed protective hood. |
The personal gem gum factory is:
The personal gem gum factory makes:
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(wiki-TODO: Nanofactory introduction infobox: both images need to go - (not anymore?)! make new better sketch of nanofactory - maybe add censored products pic - ditch or improve on covergent assemby)
What, Why, How, When
moved to main page (removed here)
Pick your favorite concern
This does not work because of ...
Friction • Thermal motion • Thermal decay at room temperature (Thermodynamics) • Fat fingers • Sticky fingers • Chicken egg problem • Nature does it differently • Quantum mechanics
For a new orientation page
Moved to: Tour by map
Misc
Refeencetests
References explained on the mediawiki wiki.
Referring to the same reference with its name: [1]
Creating a reference plus it's name: [1]
See: This works in reverse too.
PatreonBanner Template test
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