# Curved space geometry

• Coloured_muffin
In summary, the conversation discusses the concept of pi and whether its value changes in different geometric spaces. It is concluded that pi does not change, but the formulae for calculating things in different spaces may vary.

#### Coloured_muffin

If i have a volleyball and draw a circle around the centre, then draw a line between the top of the ball and the centre and measure the two line I find that the ratio circumference of the circle to diameter of the circles is 4, thus implying that in this case pi is 4, however if I drew a circle of a different size I would get a different ratio.

Could anyone tell me if the value of pi changes in curved space, or if it is the equations that need to be updated?

pi does not change. it is not defined as a ratio of anything in spherical geometry (a priori, at least). the formulae of things in spherical geometry all change: the angles of triangles no longer add to pi either.

Thanks for your help Matt, that clears up some confusion

## 1. What is curved space geometry?

Curved space geometry is a branch of mathematics that studies the properties of curved surfaces and spaces. It is based on the concept of non-Euclidean geometry, which differs from the traditional Euclidean geometry in that it allows for curves and non-linear paths.

## 2. How is curved space geometry different from Euclidean geometry?

Euclidean geometry is based on the idea that space is flat and that parallel lines never intersect. In curved space geometry, this is not the case, as parallel lines can intersect and the geometry of space can be curved or warped.

## 3. What are some real-life applications of curved space geometry?

Curved space geometry has many real-world applications, such as in physics and astronomy, where it is used to describe the curvature of space and time in Einstein's theory of general relativity. It is also used in engineering and computer graphics to design curved structures and surfaces.

## 4. Can we visualize curved space?

It can be challenging to visualize curved space, as our everyday experience is limited to flat, Euclidean space. However, we can use mathematical models and analogies to help us understand the concepts of curved space geometry.

## 5. What are some famous examples of curved space?

One of the most well-known examples of curved space is the surface of a sphere, which is a positively curved surface. Other examples include the saddle shape of a Pringles chip, which has negative curvature, and the curved space-time around massive objects like planets and stars.

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