Then, if people find errors, or have questions, they will write a comment near the content itself.
Then, next person that comes along and has the same problem, will also find that comment, and your answer will solve their problems too.
The perfect way to do this is to use GitHub issues
IAU designated constellations Updated 2025-07-16
Cover up the entire sky in a compatible way with the traditional constellations. They are also very square, the boundaries consisting only of vertical and horizontal lines on the sphere.
Ice Updated 2025-07-16
Ice is the name of one of the solid phases of water.
In informal contexts, it usually refers to the phase of ice observed in atmospheric pressure, Ice Ih.
Lebesgue integral vs Riemann integral Updated 2025-07-16
Advantages over Riemann:
Video 1.
Riemann integral vs. Lebesgue integral by The Bright Side Of Mathematics (2018)
Source.
youtube.com/watch?v=PGPZ0P1PJfw&t=808 shows how Lebesgue can be visualized as a partition of the function range instead of domain, and then you just have to be able to measure the size of pre-images.
One advantage of that is that the range is always one dimensional.
But the main advantage is that having infinitely many discontinuities does not matter.
Infinitely many discontinuities can make the Riemann partitioning diverge.
But in Lebesgue, you are instead measuring the size of preimage, and to fit infinitely many discontinuities in a finite domain, the size of this preimage is going to be zero.
So then the question becomes more of "how to define the measure of a subset of the domain".
Which is why we then fall into measure theory!
Legendre transformation Updated 2025-07-16
This is how you transform the Lagrangian into the Hamiltonian.
Figure 1.
Nelson-Mandela.jpg
. Source. Message:
"There is nothing like returning to a place that remains unchanged to find the ways in which you yourself have altered." - Nelson Mandela Nelson Rolihlahla Mandela was a South African anti-apartheid revolutionary, politician and philanthropist who served as President of South Africa from 1994 to 1999. - Wikipedia Born: July 18, 1918, Mvezo, South Africa Died: December 5, 2013.
Covering space Updated 2025-07-16
Basically it is a larger space such that there exists a surjection from the large space onto the smaller space, while still being compatible with the topology of the small space.
We can characterize the cover by how injective the function is. E.g. if two elements of the large space map to each element of the small space, then we have a double cover and so on.
Craig Silverstein Updated 2025-07-16
Video 1.
How Google began by Craig Silverstein part 1 (2006)
Source. Talk given at the University of North Carolina. A possibly official invitation from the time: www.ibiblio.org/pjones/blog/googles-craig-silverstein-at-unc-1026/.
Cray Updated 2025-07-16
Csound FLOSS manual Updated 2025-07-16
Includes introduction to the basic sound synthesis and their implementation in Csound.
Examples run on browser via Emscripten and just worked on Ubuntu 20.04!
Examples can also be downloaded all at once from: www.csound-tutorial.net/floss_manual/ Shame not in Git as standalone files.
Cycle of an element of a group Updated 2025-07-16
Take the element and apply it to itself. Then again. And so on.
In the case of a finite group, you have to eventually reach the identity element again sooner or later, giving you the order of an element of a group.
The continuous analogue for the cycle of a group are the one parameter subgroups. In the continuous case, you sometimes reach identity again and to around infinitely many times (which always happens in the finite case), but sometimes you don't.

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