Can a 4-Sphere Have a Circumference?

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SUMMARY

The circumference of a four-dimensional sphere, also known as a 4-sphere, is calculated using the formula 2πR, where R represents the radius. The surface area of a 4-sphere is given by the formula 2π²R³. The discussion highlights the relationship between the circumference and surface area formulas, emphasizing the mathematical consistency in their derivation.

PREREQUISITES
  • Understanding of basic geometry concepts
  • Familiarity with the properties of spheres in multiple dimensions
  • Knowledge of mathematical constants such as π (pi)
  • Ability to manipulate algebraic expressions involving exponents
NEXT STEPS
  • Research the properties of higher-dimensional geometry
  • Explore the mathematical derivation of the surface area of a 4-sphere
  • Learn about the implications of dimensionality in physics and mathematics
  • Study the relationship between circumference and surface area in various dimensions
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Mathematicians, physics students, and anyone interested in advanced geometry and the study of higher-dimensional spaces.

liometopum
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What is the circumference of a four dimensional sphere?
 
Physics news on Phys.org
2\pi R, I guess.
 
http://www.sjsu.edu/faculty/watkins/ndim.htm

2π2R3 is surface area.
 
Is it just coincedence that 2∏r × ∏r2 =2∏2r3
 

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