I’m seeking a physical science based explanation of why Pi equals what it does in our universe, not necessarily a mathematical answer.
What laws govern such constants…curvature of the universe? In our expanding universe, will this constant ever change?
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There is no reason, pi simply is what it is. When you divide the perimeter of a circle by its diameter, you get a very consistent yet strange number, which we called pi. It had to be something, pi is what it happens to be.
Pi equals what it does because we use a base-10 numbering system, and so the ratio of a circle’s circumference to its diameter comes out to be 3.1415927 etc.
In other bases, the number is obviously different, but it all boils down to the ratio of a circle.
The “normal” rules of geometry that people generally use have a built in assumption that all the shapes involved are sitting on a perfectly flat plane. For example, if you draw a circle onto a curved surface then measure the circumference and diameter along that surface, you will find that the equation C=pi * d doesn’t work – instead you have to use a different constant in place of pi which varies based on the exact curvature of the surface you were drawing on. That being said, the fact that the universe is growing and may have some curvature in any given spot doesn’t have any practical effect on the value of pi. You can still build an arbitrarily flat surface and not be able to feasibility detect the effects of growth and curvature
find string , make it like circle . remov string’s addition parts . Then find it’s radius .After all straighten the string , measure it’s length
so every time you will find length= 2*p*r
Cant explain without thinking mathematically to some extent. But to think about it in a different way…
Think of splitting a circle into a 4 square grid where the inside radius is the inner edge of 2 touching squares at 3, 6 9 and 12 o clock. You form a bigger square outside the circle which touches at these points.
The perimeter of this larger outer square is simply 8 times the radius, or 4 times the diameter (4 squares with 2 edges on the outer square)
The perimeter of the circle (aka its circumference) inside the square is shorter than the square, it is around 12% smaller perimeter, so rather than 4*Diameter it happens to work out at 3.14… * Diameter
If you know the “diameter” of a square (the shortest distance from one edge to the opposite edge), then the ratio of the perimeter to the diameter is 4. You could ask the same question about a hexagon, an octagon, etc. — the number approaches 3.14159…. etc as the number of sides gets big.
math is a way of simplifying reality to make it easier to understand.
no rule in math affects reality, it’s reality that math is just trying to understand.
example you could make a ‘rule’ in math that simplifies how long an apple takes to grow, be eaten and how much money it makes. but that rule is dependent on variables, and within those variables are more variables and the deeper we get into science the more likely we are to realize the complexity of the universe is beyond mathematics. (example:how fast an apple grow depends on the tree, soil content, amount of rain, amount of sun. then we break down each of those variables, say sun(position on earth, amount of cloud cover and terrain, and solar activity) then we break that down again into why cloud cover(solar storms, industrial outputs, magnetic fields generated by earths core on and on and on)on and on and on) on and on and on. mathematic rules are not accurate, however they are tools to help simplify reality into a usable form for the human mind.
You know how math is reversible? Like, not only does 2 × 2 = 4, but also 4 ÷ 2 = 2?
How π is found is just reversing the numbers in a similar way. You can measure the radius of a circle. You can measure the circumference. If you have those two values, you can calculate π. Other constants are discovered in similar ways.
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