Calabi-Yau Manifolds

Calabi-Yau manifolds are complex, multi-dimensional shapes used in string theory to describe the hidden, compact dimensions of the universe. While we perceive the universe in three dimensions, these manifolds have six or seven additional curled-up dimensions with intricate geometric structures. Their unique properties allow strings—fundamental building blocks in physics—to vibrate in consistent ways, influencing particles and forces we observe. Essentially, Calabi-Yau manifolds provide a mathematical framework for understanding how extra dimensions shape the fundamental nature of reality.