mathswithmuza on Instagram: "The Costa surface is a remarkable example of a minimal surface—a surface that locally minimizes area, meaning its mean curvature is zero everywhere. Discovered by the Brazilian mathematician Celso Costa in 1982, this surface beautifully bridges the geometry of classical minimal surfaces like the catenoid and helicoid. It has the topology of a torus with three punctures, which can be thought of as a donut shape with three holes extending to infinity. What makes it esp

mathswithmuza on Instagram: "The pseudosphere is a fascinating geometric surface that represents constant negative curvature—meaning that every point on the surface curves away from itself in all directions, similar to a saddle shape. It is generated by rotating a tractrix (a special curve where the tangent length to an asymptote is constant) around its asymptote. This process creates a surface that serves as a model for hyperbolic geometry, where the usual rules of Euclidean geometry no longer

Explaining The Universe on Instagram: "All of Earth’s water, known as the hydrosphere, covers about 71% of the planet’s surface and exists in many forms — oceans, lakes, rivers, ice, groundwater, and even water vapor in the atmosphere. About 97% of it is salt water found in the oceans, while only about 3% is fresh water. Most of that fresh water is locked in glaciers and ice caps, mainly in Antarctica and Greenland. Less than 1% of Earth’s total water is available as liquid fresh water in rivers