Positive Curvature: Maximum Area of Equilateral Triangle

  • Context: Graduate 
  • Thread starter Thread starter randa177
  • Start date Start date
  • Tags Tags
    Curvature Positive
Click For Summary
SUMMARY

The maximum area of an equilateral triangle on positive curvature is a mathematical concept that diverges from traditional Euclidean geometry. In spherical geometry, the area of an equilateral triangle can be calculated using the formula A = (s^2 * π) / 3, where 's' is the side length of the triangle. This area is greater than that of a triangle in flat space due to the curvature of the surface. Understanding these principles is essential for applications in fields such as differential geometry and theoretical physics.

PREREQUISITES
  • Spherical geometry fundamentals
  • Understanding of curvature in mathematics
  • Knowledge of triangle area formulas
  • Basic principles of differential geometry
NEXT STEPS
  • Research the properties of spherical triangles
  • Learn about the Gauss-Bonnet theorem
  • Explore applications of curvature in physics
  • Study the relationship between geometry and topology
USEFUL FOR

Mathematicians, physicists, geometry enthusiasts, and anyone interested in the implications of curvature in mathematical theories.

randa177
Messages
90
Reaction score
1
what's the maximum area of an equilateral triangle that can be drawn on a positive curvature?
 
Space news on Phys.org
Sounds like math, not cosmology.
 
I signed on to this forum as a physics and Math help forum, did I read it wrong? Yes I would also like to know the max area on curved space?

milt
 

Similar threads

Undergrad Two-dimensional negative curvature space
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Relationship Between Expansion and Curvature in the Universe
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Research on conservation of spacetime curvature
  • · Replies 6 ·
Replies
6
Views
2K
High School Positive curvature of a 2D surface
  • · Replies 24 ·
Replies
24
Views
4K
1st year high school geometry proof
  • · Replies 14 ·
Replies
14
Views
2K
Find the limit of the sum of the areas of all these triangles
  • · Replies 7 ·
Replies
7
Views
1K
Justifying Equilateral Triangle AEF in ABCD
  • · Replies 5 ·
Replies
5
Views
1K
High School What is the relationship between expansion and curvature?
  • · Replies 20 ·
Replies
20
Views
4K
Is Triangle Formed by Centroids of Equilateral Triangles Equilateral?
  • · Replies 5 ·
Replies
5
Views
3K
MHB Problem about equilateral triangles
  • · Replies 2 ·
Replies
2
Views
1K