The definition is to take the vector space, remove the zero element, and identify all elements that lie on the same line, i.e.
The most important initial example to study is the real projective plane.
Cav2.1, also known as P/Q-type calcium channels, is a member of the voltage-gated calcium channel family. These channels are critical for various physiological processes, including neurotransmitter release, muscle contraction, and other cellular signaling mechanisms. Cav2.1 channels are primarily found in the central nervous system and at the neuromuscular junction. The term "Cav2.
Web of Stories 1997 interview playlist: www.youtube.com/playlist?list=PLVV0r6CmEsFxKFx-0lsQDs6oLP3SZ9BlA
The way this dude speaks. He exhales incredible intelligence!!!
In the interviews you can see that he pronounces names in all languages amazingly, making acute effort to do so, to the point of being notable. His passion for linguistics is actually mentioned on Genius: Richard Feynman and Modern Physics by James Gleick (1994).
Maybe this obsession is partly due to his name which no English speaking person knows how to pronounce from the writing.
This passion also led in part for his names to some physics terminology he worked on winning out over alternatives by his collaborators, most notably in the case of the naming of the quark.
Small microscopic visible particles move randomly around in water.
If water were continuous, this shouldn't happen. Therefore this serves as one important evidence of atomic theory.
The amount it moves also quantitatively matches with the expected properties of water and the floating particles, was was settled in 1905 by Einstein at: investigations on the theory of the Brownian movement by Einstein (1905).
This suggestion that Brownian motion comes from the movement of atoms had been made much before Einstein however, and passed tortuous discussions. Subtle is the Lord by Abraham Pais (1982) page 93 explains it well. There had already been infinite discussion on possible causes of those movements besides atomic theory, and many ideas were rejected as incompatible with observations:The first suggestions of atomic theory were from the 1860s.
Further investigations eliminated such causes as temperature gradients, mechanical disturbances, capillary actions, irradiation of the liquid (as long as the resulting temperature increase can be neglected), and the presence of convection currents within the liquid.
Tiny uniform plastic beads called "microbeads" are the preferred 2019 modern method of doing this: en.wikipedia.org/wiki/Microbead
Original well known observation in 1827 by Brown, with further experiments and interpretation in 1908 by Jean Baptiste Perrin. Possible precursor observation in 1785 by Jan Ingenhousz, not sure why he wasn't credited better.
Observing Brownian motion of micro beads by Forrest Charnock (2016)
Source. Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact