# Ellipses have multiple definitions, how are these the same?

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/pQa_tWZmlGs The full video this comes from proves why slicing a cone gives the same shape as the two-thumbtacks-and-string construction, which is beautiful. Editing from long-form to short by Dawid Kołodziej

# Three levels of understanding Bayes’ theorem

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/HZGCoVF3YvM Editing from long-form to short by Dawid Kołodziej

From 3Blue1Brown. A link to the full video about Bayesian thinking is at the bottom of the screen. Or, for reference: https://youtu.be/lG4VkPoG3ko Long-to-short editing by Dawid Kołodziej

# Positioned as the hardest question on a Putnam exam (#6, 1992)

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/OkmNXy7er84 Editing from the original video into this short by Dawid Kołodziej

# Why does light slowing imply a bend? (Beyond the tank/car analogy)

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/Cz4Q4QOuoo8 That video answers various viewer questions about the index of refraction. Editing from long-form to short by Dawid Kołodziej

# What does it mean that light “slows down” in glass?

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/KTzGBJPuJwM That video unpacks the mechanism behind how light slows down in passing through a medium, and why the slow-down rate would depend on color. Editing from long-form to short by Dawid Kołodziej

# Definition of a “bit”, in information theory

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/v68zYyaEmEA That video describes using information theory to write a bot that plays Wordle Editing from long-form to short by Dawid Kołodziej

# What is a group?

From 3Blue1Brown. A link to the full video is at the bottom of the screen. Or, for reference: https://youtu.be/mH0oCDa74tE That video introduces group theory and the monster group. Editing from long-form to short by Dawid Kołodziej