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

  • Thread starter Vebjorn
  • Start date
In summary, the conversation involves a 15-year-old preparing for a road trip and looking for equations to solve to keep busy. Some suggested equations include calculating the Earth and moon's orbit velocities, the relationship between gravitational acceleration and mass and radius, and the approximate mass of the Earth and sun using orbit parameters. They also mention a problem called Fermat's last theorem, which remained unsolved for centuries until it was solved by Andrew Wiles.
  • #1
Vebjorn
6
0
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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  • #2
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.
 
  • #3
Thank you! I leave in about 10 minutes! :)
 
  • #4
Try this cute problem. Given the equation

[tex] a^n + b^n = c^n [/tex]

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.
 
  • #5
Wallace said:
Try this cute problem. Given the equation

[tex] a^n + b^n = c^n [/tex]

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.
 
  • #6
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.
 

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

1. What is the purpose of using equations on a road trip?

The purpose of using equations on a road trip is to calculate important information such as distance, time, speed, and fuel consumption. These calculations can help plan the route, estimate travel time and budget, and optimize the trip for efficiency.

2. How can equations help with navigation during a road trip?

Equations can help with navigation by providing precise measurements and calculations for distance and time. This information can be used to estimate arrival times, plan rest stops, and choose the most efficient routes.

3. What are some common equations used during a road trip?

Some common equations used during a road trip include distance = speed x time, average speed = total distance / total time, and fuel efficiency = distance / fuel consumption. Other equations may be used for specific purposes, such as calculating toll costs or estimating the number of miles per gallon for a vehicle.

4. Can equations be used for unexpected events during a road trip?

Yes, equations can be used for unexpected events during a road trip. For example, if there is a detour, the distance and time can be recalculated to adjust the route. If there is heavy traffic, the average speed can be adjusted to estimate a more accurate arrival time. Equations can also be used to calculate necessary expenses for unexpected events, such as a flat tire or emergency repairs.

5. How can equations be used to save money during a road trip?

Equations can help save money during a road trip by optimizing the route for efficiency and estimating fuel costs. By calculating the most efficient route and adjusting for factors such as traffic and tolls, the total distance and fuel consumption can be minimized, ultimately saving money. Equations can also be used to estimate overall trip expenses and create a budget for the trip.

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