I worked through this presentation slowly to present the material to high school maths students and found the section on calculating the circumference of the earth very accessible, but would be good if you explained how Aristarchus calculated the diameter of the moon through trigonometry.
For Plutophiles you might mention Pluto is still more than a rock, it is a Dwarf Planet, since it has not cleared the debris in its orbit, but this means in future it could become reclassified as a planet.
Beautyfull lesson ! Thank' s Nornan About Platone residence in Siracusa we know that he was invited by the Dionisio and after a conversation about Virtue the tyrant was so irritated by the philosopher to sell him as a slave, Then the story goes on....
dear mr. wildberger, is it also possible to make a video about how kepler discovered that the orbits are not circles but ellipses? I have never seen that explained clearly. also, there is a paper by curtis wilson, "the great inequality of jupiter and saturn from kepler to laplace". maybe it may give an idea about a future famousmathprobs :-). anyways, thanks for the extremely beautiful presentation.
During the true total solar eclipse I saw in the middle of it it got pretty dark and all the crickets started in like they would at nighttime and the birds and everything it was great.
There is one observable problem. Shadows do not act like perspective. From a single light source( the sun, for example) any object in the light will block the area that is the 2-dimensional shape and size of that object. The "tunnel" of shadow will continue through space until an object intercepts it. The area this shadow covers will be exactly the same size and shape as the object blocking the light. Perspective, on the other hand, is the apparent reduction in size of an object as the distance increases. Thus, it is due to perspective that the moon, though much smaller than the sun can eclipse the sun. This would be easy to verify. The totality of a solar eclipse can be seen over a very small area compared to Earth. If a group of observers photographed the eclipse from locations at the edges of the shadow they could calculate the exact size of the moon. This would let them find the true distance to the moon, knowing it's apparent size is a half degree. It will be found to be less than 4000miles(6436km) away. You can see my example on you tube "math challenges the moon landings". Also see www.crystalcodex.com for more stuff.
Goldspotter The Greeks had different views. Aristarchus proposed the heliocentric theory around 200 BC, but it was not widely accepted. But definitely the idea was around then.
I worked through this presentation slowly to present the material to high school maths students and found the section on calculating the circumference of the earth very accessible, but would be good if you explained how Aristarchus calculated the diameter of the moon through trigonometry.
excellent excellent presentation
Well done
Thank you for these great lectures
Your great math teacher god bless you
Thank you very much! I will purchase your PDFs!
For Plutophiles you might mention Pluto is still more than a rock, it is a Dwarf Planet, since it has not cleared the debris in its orbit, but this means in future it could become reclassified as a planet.
This should have more views,.. great lecture
Beautyfull lesson ! Thank' s Nornan
About Platone residence in Siracusa we know that he was invited by the Dionisio and after a conversation about Virtue the tyrant was so irritated by the philosopher to sell him as a slave, Then the story goes on....
Very clear explanation -- thank you, mr. Wildberger.
dear mr. wildberger,
is it also possible to make a video about how kepler discovered that the orbits are not circles but ellipses? I have never seen that explained clearly.
also, there is a paper by curtis wilson, "the great inequality of jupiter and saturn from kepler to laplace". maybe it may give an idea about a future famousmathprobs :-).
anyways, thanks for the extremely beautiful presentation.
Carl Sagan's 1980 "Cosmos" series has a whole episode on this.
Great video. Takes me back to my university astronomy classes.
Wow so ur an astronomer?
@@relaxedpsycho4747 amateur, not professional
During the true total solar eclipse I saw in the middle of it it got pretty dark and all the crickets started in like they would at nighttime and the birds and everything it was great.
There is one observable problem. Shadows do not act like perspective. From a single light source( the sun, for example) any object in the light will block the area that is the 2-dimensional shape and size of that object. The "tunnel" of shadow will continue through space until an object intercepts it. The area this shadow covers will be exactly the same size and shape as the object blocking the light. Perspective, on the other hand, is the apparent reduction in size of an object as the distance increases. Thus, it is due to perspective that the moon, though much smaller than the sun can eclipse the sun. This would be easy to verify. The totality of a solar eclipse can be seen over a very small area compared to Earth. If a group of observers photographed the eclipse from locations at the edges of the shadow they could calculate the exact size of the moon. This would let them find the true distance to the moon, knowing it's apparent size is a half degree. It will be found to be less than 4000miles(6436km) away. You can see my example on you tube "math challenges the moon landings". Also see www.crystalcodex.com for more stuff.
You've got it all wrong: www.timeanddate.com/eclipse/umbra-shadow.html
But the Greeks did not know planets revolve around the Sun ...
Goldspotter The Greeks had different views. Aristarchus proposed the heliocentric theory around 200 BC, but it was not widely accepted. But definitely the idea was around then.
Watapon, Religion and due to the fact that tools such as the telescope were not yet existent.