Are there any equations I can solve on a 10-hour road trip?

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A user is seeking simple and engaging equations to solve during a 10-hour road trip in Norway, mentioning previous calculations like the gravitational pull between the moon and Earth. Suggestions include finding the Earth's orbital velocity around the sun, calculating the moon's orbit, and deriving gravitational acceleration related to mass and radius. A more complex challenge discussed is Fermat's Last Theorem, which states that there are no integer solutions for the equation a^n + b^n = c^n when n is greater than 2. The discussion highlights a mix of simple and complex mathematical problems suitable for a young learner. Engaging with these equations can provide an enjoyable way to pass the time on the trip.
Vebjorn
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Hi! I am going on a 10 h road trip further north in Norway tomorrow, does anyone here have some fun equations i can solve? I mean, simple equations. I calculated the gravitational pull between the moon and the Earth (Quite a big number i must say) Those kind of things, the equation to calculate the Earth's rotation speed? Anything that can keep me busy! I also appreciate some complicated equations as well, but not too complicated as i am 15 years old and internet is a bit of a problem in the car!

- Vebjorn
 
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Find the velocity of the Earth's orbit around the sun (simple enough, probably simplest).

If you like velocities, then calculate the same thing for the moon's orbit around the Earth.

Find the equation that relates gravitational acceleration (g - 9.81 m/s^2 on Earth) to mass and radius.

Find an approximate value for the mass of the Earth using the moon's orbit parameters (little more involved).

Repeat the same for the sun's mass and the Earth's orbit parameters.
 
Thank you! I leave in about 10 minutes! :)
 
Try this cute problem. Given the equation

a^n + b^n = c^n

is it possible to have a solution if a, b and c are all integers for any n>2? I have this neat proof that no solutions exist, but there isn't enough space left in this post to write it down.
 
Wallace said:
Try this cute problem. Given the equation

a^n + b^n = c^n

is it possible to have a solution if a, b and c are all integers for any n>2? I have this neat proof that no solutions exist, but there isn't enough space left in this post to write it down.


Hm, I'm not sure i got the question and I am not sure what integers means. Maybe that's why :P I'll look it up.
 
Sorry, my previous post was a bad joke. This puzzle is known as Fermat's last thereom, and it remained unsolved for many centuries. It was solved a few years ago but I think the consensus is that the current best solution is not very elegant, and a better one is still sought. Look up the history of the problem (google, wiki...) as it is a classic bit of mathematics history.
 

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