Uploaded July 2018 | Updated September 2026, 1 week ago
A closer look at the Moon Tilt (or Moon Terminator) Illusion digging deep into the math.
Math is the language of science. If I can science that, then I should be able to math it!
skip ahead:
@0:23 Video showing example of the illusion
@1:44 Simulation of the illusion (from my previous video on this)
@2:43 New simulation - this time to scale
@4:54 Introducing the paper
@5:44 tl;dr just give me the answer please
@8:15 Going through all the math in the paper
@21:20 The first time we see the answer in the paper
@22:04 Reducing and simplifying the equation
@26:41 Going through Appendix A in the paper
@31:31 Putting it in terms of the input angles
@31:56 Going through Appendix B in the paper
@36:56 The final answer for "alpha" - the apparent direction of the light
@37:13 Showing the angle in the 3D sim
@41:09 Demonstrating that the answer is independent of the distances. It is based only on the angles
@42:30 Getting the "beta" from the paper - the expected lighting angle
@45:19 Appendix C from the paper
@47:29 Putting "beta" in terms of the input angles
@47:35 Appendix D from the paper
@48:49 The final form of "beta"
@49:18 A different approach... matrix transformations
@50:30 Looking at the new approach in the 3D sim
@51:14 Why all this math?
@52:19 Summary
Featured Content:
Example of Moon Tilt Illusion (Warning: Language... watch muted): youtube.com/watch?v=peKlRl9sxc4
Paper detailing the math behind the illusion: http://www.seas.upenn.edu/~amyers/MoonPaperOnline.pdf
Featured Software:
Unity3D unity3d.com
Stellarium stellarium.org
Errata:
I made a mistrake and put the sun at -0.24 instead of 0.24.
The correct angle should have been 41.47979 rather than the 42.15258 shown in the video. I'm not going to redo the whole video for 0.7 degrees on an angle over 40 degrees.
Also I said, "ascension" instead of "elevation". My bad.
A closer look at the Moon Tilt (or Moon Terminator) Illusion digging deep into the math.
Math is the language of science. If I can science that, then I should be able to math it!
skip ahead:
@0:23 Video showing example of the illusion
@1:44 Simulation of the illusion (from my previous video on this)
@2:43 New simulation - this time to scale
@4:54 Introducing the paper
@5:44 tl;dr just give me the answer please
@8:15 Going through all the math in the paper
@21:20 The first time we see the answer in the paper
@22:04 Reducing and simplifying the equation
@26:41 Going through Appendix A in the paper
@31:31 Putting it in terms of the input angles
@31:56 Going through Appendix B in the paper
@36:56 The final answer for "alpha" - the apparent direction of the light
@37:13 Showing the angle in the 3D sim
@41:09 Demonstrating that the answer is independent of the distances. It is based only on the angles
@42:30 Getting the "beta" from the paper - the expected lighting angle
@45:19 Appendix C from the paper
@47:29 Putting "beta" in terms of the input angles
@47:35 Appendix D from the paper
@48:49 The final form of "beta"
@49:18 A different approach... matrix transformations
@50:30 Looking at the new approach in the 3D sim
@51:14 Why all this math?
@52:19 Summary
Featured Content:
Example of Moon Tilt Illusion (Warning: Language... watch muted): youtube.com/watch?v=peKlRl9sxc4
Paper detailing the math behind the illusion: http://www.seas.upenn.edu/~amyers/MoonPaperOnline.pdf
Featured Software:
Unity3D unity3d.com
Stellarium stellarium.org
Errata:
I made a mistrake and put the sun at -0.24 instead of 0.24.
The correct angle should have been 41.47979 rather than the 42.15258 shown in the video. I'm not going to redo the whole video for 0.7 degrees on an angle over 40 degrees.
Also I said, "ascension" instead of "elevation". My bad.
