Adding up Integers and Cubes the easy way! @yourfavouriteta

Uploaded August 2020 | Updated September 2026, 2 weeks ago

The video was created using manim - a python-based animation library created by Grant Sanderson (3blue1brown).

I installed manin using the following guide by Flammable Maths and vcubingx:
youtube.com/watch?v=Jfgtl-AW5Oc

For helpful tutorials on how to use manim, please check out Theorem of Beethoven:
youtube.com/channel/UCxiWCEdx7aY88bSEUgLOC6A

Adding up Integers and Cubes the easy way!

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$Phase- and frequency noise spectra explained! Link to python notebook used for simulations: https://github.com/OleKrarup123/NLSE-vector-solver/tree/main/TutorialVideos/PhaseAndFreqNoise-Video General explanation of amplitude, phase and frequency noise: https://ieeexplore.ieee.org/document/9973001 Explanation of electric field spectrum measurement and phase noise: https://www.youtube.com/watch?v=hfgaEjf1154 Thorough explanation of phase and frequency noise: https://silentsys.com/white-papers/laser-noise-metrological-metrics In-depth explanations of phase noise: https://www.youtube.com/watch?v=ggPdXWejMb8 https://youtu.be/qPUEhBeG2zM?is=ZOxWMkkv52HX3iv2 https://books.google.dk/books?id=iUld6xblvo0C&pg=PA45&source=gbs_toc_r&cad=2#v=onepage&q&f=false https://www.youtube.com/watch?v=McTOAFFK74s Examples of 1/f behavior: https://dsp.stackexchange.com/questions/74816/signal-of-frac1f-noise https://arxiv.org/pdf/physics/0204033 https://ieeexplore.ieee.org/document/1456550 https://www.analog.com/en/resources/analog-dialogue/articles/understanding-and-eliminating-1-f-noise.html Phase noise application notes: https://www.nktphotonics.com/wp-content/uploads/2022/01/koheras-laser-phase-noise.pdf Freq. noise application notes: https://www.nktphotonics.com/wp-content/uploads/2022/01/frequency-stability-application-note-version-1-1-.pdf https://www.researchgate.net/publication/282135028 https://www.koheron.com/blog/2021/07/08/measuring-laser-phase-noise/$

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Adding up Integers and Cubes the easy way!