Math Mornings Online: Spherical Triangles

Instead of our live lectures in Davies Auditorium, here is a short video about one of my favorite theorems about the sphere!
Math Mornings is a series of lectures organized by the Yale Mathematics Department for New Haven area families. See here for more:

[michaeldamolsen]

Thanks for this video Yair, it was a real pleasure to watch. Such a shame that you haven't found time to make more.

[carmelpule]

What I am admiring is how this gentleman in the video is so elegantly dealing with,

1. An invisible and silent REAL function being processed on the surface of a sphere, which does not need any humans to support it.
2. To project it in visual form so that human eye can see and understand it with the use, the mathematical ARTIFICIALLY INVENTED DRAWN symbols/ images/shadows of reality, representing the REAL silent surface operation, in that, the first area, due to one angle covering the whole area of the sphere, then the second area with the second angle covering the whole are plus two triangles, and the third area due to the third angle covering the whole area plus two triangles, hence the total area equals 4^A1 +4*A2 + 4*A3 = 4*pi + 4( area of triangle)
2. To project it so that the human ear can understand the sequence of events, then there are the ARTIFICIALLY INVENTED LANGUAGE sound symbols/images, shadows of the reality representing the invisible and silent truth of the function being active on the surface of that sphere.

I have followed some other tuition on this subject, and some people correctly refer to the angle in the small triangle as A1, A2, A3 "as angles" but refer to the opposite arcs as "lines " as a1, a2, a3, when they should refer to these as angles subtended at the centre of a unit sphere.
Congratulations and well done.
Perhaps instead of using one drawing to show "in parallel "the three double lunes superimposed on one sphere, one could have drawn three separate diagrams in sequence, to complement the sequential launched series information of a language projection which the ear needs to handle, The eye can handle parallel information but for a new comer it would have been an advantage to ask the eye to follow a series input information!! rather than the parallel information shown at 21:58.
Esculent presentation thank you for distributing this work.

[meleknurgorgun]

Thank you so much for the video🙌🌺 I am currently studying for spherical astronomy final exam and this video helped me a lot 💯

[اممدنحمظ]

فيديو جميل طيب . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا. تحياتنا لكم من غزة فلسطين .

[aaaaaa-rrxm]

1:25 I think he meant (a+b+c-pi)r^2 is the area

[jacobolus]

This theorem is usually attributed to Albert Girard (1629), from a century and a half before the birth of Gauss.

[yairmin]

Here are the links mentioned in the video:

[hellolello]

I would assume that by pi he means in radians, not degrees

[TomFaulkenberry]

Yair, this is a great lecture! I would love to know what setup you used for the video, and particularly, what app you are using for your notes. Thanks!