# Physics based programming problem sets

• hudsonj
In summary, the conversation revolved around the search for resources similar to the website "Project Euler" but with a focus on physics topics. The conversation also touched upon the different categories of problems in physics and mathematics, with a mention of the unsolved problem of finding the nth prime number. The individual looking for resources clarified that they were interested in finding physics-themed problem solving activities that require or encourage the use of programming.

#### hudsonj

TL;DR Summary
Looking for resources similar to the website "Project Euler" but based around physics topics.
Was wondering if anyone knew of any good resources with programming challenges akin to the website "Project Euler" (about page found here). To be more specific, I'm looking for something consisting of problems centred around physics topics that would require some level of problem solving and programming to solve in a reasonable time frame, i.e. deriving and algorithm for finding the nth prime number instead of just listing them off.

hudsonj said:
TL;DR Summary: Looking for resources similar to the website "Project Euler" but based around physics topics.
I don't think there are any. This is because we can categorise problems in Physics as follows:
• Problems with an analytic solution
These do not need programming skills to solve.
• Problems with a deterministic solution
These are described with differential equations so the programming skills required to solve are "write an algorithm to solve differential equations". This is an interesting and complicated problem in its own right, but it would not make a very interesting series of challenges. If you are interested in writing programs to solve differential equations you should study this topic, not try to work out algorithms yourself.
• Problems without a deterministic solution
Techniques do exist to model these, however as there is no deterministic solution how would the website check your results?

I am confused by your reference to
hudsonj said:
deriving and algorithm for finding the nth prime number instead of just listing them off.
This is not a problem "centered around a physics topic". Also note that it is an unsolved (and generally believed to be unsolvable) problem in mathematics.

• pbuk said:
I don't think there are any. This is because we can categorise problems in Physics as follows:
• Problems with an analytic solution
These do not need programming skills to solve.
• Problems with a deterministic solution
These are described with differential equations so the programming skills required to solve are "write an algorithm to solve differential equations". This is an interesting and complicated problem in its own right, but it would not make a very interesting series of challenges. If you are interested in writing programs to solve differential equations you should study this topic, not try to work out algorithms yourself.
• Problems without a deterministic solution
Techniques do exist to model these, however as there is no deterministic solution how would the website check your results?

I am confused by your reference to

This is not a problem "centered around a physics topic". Also note that it is an unsolved (and generally believed to be unsolvable) problem in mathematics.
That's a shame.

The reference I gave was the description of one of the problems found on the websites archive, which you can find here, and is very much solvable.

My intention was to give an example of the type of problem(s) I was looking for, being the creative application of the user's understanding of programming and the relevant topic(s) to solve a problem that would otherwise be cumbersome or even impossible to solve without a computer.

So really, I'm looking for physics themed problem solving activities that require or at least heavily encourage some level of programming to solve in a reasonable time span, as is the intention of Project Euler but with an emphasis on topics within maths, sorry for any misunderstanding.

We had a problem one time in Classical Mechanics class that called for a numerical solution and everyone was of the opinion that there was no analytic one until a student produced it. Everyone was amazed but looking back some years earlier, the prof found that another person had discovered it first.

The suspicion was that the authors of the book knew it but felt this particular problem was ideal for teaching numerical problem solving and so never mentioned that one existed.

hudsonj said:
The reference I gave was the description of one of the problems found on the websites archive, which you can find here, and is very much solvable.
Yes I am familiar with Project Euler. Problem 7 is of course solvable: we find the Nth prime by counting primes until we get to N, in other words by listing them off. But you suggested that you could find
hudsonj said:
[an] algorithm for finding the nth prime number instead of just listing them off.

hudsonj said:
My intention was to give an example of the type of problem(s) I was looking for, being the creative application of the user's understanding of programming and the relevant topic(s) to solve a problem that would otherwise be cumbersome or even impossible to solve without a computer.
Yes, there are lots of such problems in Maths. (Deterministic) Problems in Physics fall into the following categories:
• finding the root(s) of an equation
• finding eigenvalues of a matrix
• finding the solution to a set of simultaneous equations
• integrating a set of ordinary differential equations
• integrating a set of partial differential equations
None of these require any "creative application of the user's understanding of programming", they just require the abilities to know which algorithm to apply from a library and to configure the problem to fit the library's API.

If you disagree, perhaps you could give an example of a problem in Physics that suits your criteria, and we can suggest somewhere you might find other such problems.

• hudsonj

## 1. What is physics-based programming?

Physics-based programming refers to using principles and laws from physics to design and develop computer programs. It involves using mathematical and scientific concepts to build simulations, games, and other applications that accurately model real-world physics.

## 2. What are some common programming problems in physics-based programming?

Some common programming problems in physics-based programming include collision detection, gravity simulation, and creating realistic physics interactions between objects. These problems often require a deep understanding of physics concepts and strong mathematical skills.

## 3. How can I improve my physics-based programming skills?

To improve your physics-based programming skills, it is important to have a strong foundation in both physics and programming. You can also practice by working on projects and challenges that involve physics-based programming, and seeking out resources and tutorials to learn new techniques and concepts.

## 4. What are some applications of physics-based programming?

Physics-based programming is used in a wide range of applications, including video games, simulations for scientific research, and virtual reality experiences. It is also used in industries such as aerospace, engineering, and robotics to model and test the physical behavior of systems.

## 5. Are there any programming languages specifically designed for physics-based programming?

While there are no programming languages specifically designed for physics-based programming, there are some languages that are commonly used for this purpose. These include C++, Python, and Java, as they have strong mathematical capabilities and can handle complex physics calculations efficiently.