OT: Really cool thing I came upon this morning. Math related. (Fair warning.)

[LionJim]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

 

[anon_xdc8rmuek44eq]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

 

[Woodpecker]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

I thought Khinchin was this guy ... nevermind

 

[LafayetteBear]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

SmithtonLion approved this ^^^^ post.

 

[lionroar88]

Pretty much!

206/7 = 29.43

That is simply awesome.

 

[LionJim]

 

[T J]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

Huygens' work was astronomically impressive.

Q: How to determine gearing that represents Saturn's orbit?

A: Unless it's over your head, carefully Planet to take up the space.

Einstein developed a theory about space too, and it was about time.

​

 

[step.eng69]

UP URANUS dwarf,

 

[anon_xdc8rmuek44eq]

 

[anon_xdc8rmuek44eq]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

The best Sci-Fi show on TV is Rick and Morty. You should watch it (it's has a lot of, um, *crude*, humor, but still - you're an adult!), especially the episode called 'A Rickle In Time' where the show deals with both Heisenberg's Uncertainty Principle and Schrodinger's Cat. It's so dumb it's smart though, you know? Has a 9.4 rating on IMDB and a 97% on Rotten Tomatoes.

Here is Rick explaining how he and his grandkids are in overlapping timelines of uncertainty.

 

[mn78psu83]

A neutrino walks "through" a bar.

 

[ClarkstonMark]

I find the gear ratio calculation pretty elementary.
Figuring out how long it takes Saturn to orbit the sun - now that is impressive.

 

[mn78psu83]

Copied from the link:

Huygens was building a mechanical model of the solar system and wanted to design the gear ratios to produce a proper scaled version of the planetary orbits. So, for example, in Huygens' day it was thought that the time required for the planet Saturn to orbit the Sun is

years (it is now known to be

years). In order to model this motion correctly to scale, he needed to make two gears, one with

teeth, the other with

teeth, so that

is approximately

. Since it is hard to fashion small gears with a huge number of teeth, Huygens looked for relatively small values of

and

. He calculated the continued fraction expansion of

and read off the first few rational approximations:

. Thus, to simulate accurately Saturn's motion with respect to that of the Earth's, Huygens made one gear with

teeth and the other with

teeth.

This might be the least interesting part of the whole post.

Anyway....

Beat Michigan.

I am no mathematician or scientist. I have a lot of curiosity though and I read all of the examples. My favorite genius of all-time is probably Gauss. I love when I read things like this:

"The general pattern of cfes was first discovered in 1812 by the great German mathematician Carl Friedrich Gauss(1777-1855), but (typically) he didn't publish his findings. Instead, he merely wrote to Pierre Laplace in Paris telling him what he had found ..."

How immense was this man's mathematical ability? There are so many examples like this from his life. He just didn't have enough time to work out everything he imagined. Just remarkable.

 

[Leo Ridens]

A neutrino walks "through" a bar.

Well played, sir, well played.

 

[lj4heisman1]

fake news....neutrinos are not faster than light

pretty funny poster anyway

 

[LionJim]

I find the gear ratio calculation pretty elementary.
Figuring out how long it takes Saturn to orbit the sun - now that is impressive.

On the other side of the coin, consider the Planck Epoch, which is the time from the Big Bang until light traveled one Planck Unit. Given that the diameter of a proton is 10^20 Planck Units, one second is equal to the elapsed time of 10^43 Planck Epochs. That's equally impressive.

 

[T J]

On the other side of the coin, consider the Planck Epoch, which is the time from the Big Bang until light traveled one Planck Unit. Given that the diameter of a proton is 10^20 Planck Units, one second is equal to the elapsed time of 10^43 Planck Epochs. That's equally impressive.

Planck's his genius was epic. ​