# Original Problem! Expanding Galaxies and Rates of Change

Afiq Hatta here presents a nice little problem that mixes geometry and calculus. And it’s inspired by cosmology, to cover an extra subject.

## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

## 6 thoughts on “Original Problem! Expanding Galaxies and Rates of Change”

1. Hi Joseph
You need to explain to “The Malaysian Mathematics” that there is a world (universe) of difference between his formulation of the problem, with its constant rates of change for a, b and c, and an expansion, in which the rate of displacement of two points is proportional to the current displacement.
In the constant case the triangle will eventually become equilateral, in the expansion case the shape of the triangle remains the same and its rate of expansion is proportional to the square of the displacement.
You can do the math!

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1. afiqhatta says:

You are totally correct howardat58 – but it depends on the model of cosmological expansion used! That’s why I said *almost*. I am actually working on a problem which will include a d|AC|/dt = k * AC, and so on. Thank you for your feedback! It is only inspiration, not a following. Sorry once again – I may even edit the point. Of course if you really wanted to go into detail you could include relativity and so forth, depending on what model (Steady state/ etc.) of expansion you wish to cover! Hey if you would like to collaborate….

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1. I probably ought to have explained more in my introduction that I understood this was a problem inspired by cosmological expansion rather than directly drawn from it. A good problem can come from even an unrealistically loose model.

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2. J. Sánchez says:

Nice post. I like this type of problems because it could make the students more enthusiasts with calculus. I mean, when someone ask to the student: What are you studying in calculus? R/ Something with expanding galaxies.

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1. I’d like to think so. It’s an imagination-capturing sort of problem, at least, even granting that the relationship to actual galaxy behavior is slight. It’s hard to find problems that are both about stuff people naturally want to know more about and that fit neatly a particular problem to solve.

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