Hyperbolic slit

1. Content

Exhibitions consist of hyperbolic slits with planar structures and single leaf hyperbolic models with three-dimensional structures. Through hands-on experience and observation, as well as a combination of planar and three-dimensional methods, they allow the audience to understand that hyperbolic slits are an interesting scientific experiment and cultivate their interest in scientific mathematics research.

Approaching the interactive area of the exhibition items, the audience can try pulling a straight stick to see what phenomena appear. The audience can also turn the handwheel to observe the changes in the single leaf hyperbolic model.

Through interaction, we found that a straight rod can easily pass through an "X" shaped slit, and mathematical knowledge tells us that this slit is a hyperbolic slit. The trajectory traced by a rotating straight rod in the air is called a hyperbolic solid shape, and the line drawn along the curved edge from the top to the bottom of the hyperbolic surface is called a hyperbola. The curve carved on this platform is also called a hyperbola, which is itself part of the straight rod's rotation trajectory. Therefore, when the straight rod rotates, it can cleverly pass through the curved slit. For a surface, if there is a straight line passing through every point on the surface, we call it a ruled surface. Cylindrical surfaces and single leaf bipartite surfaces are both ruled surfaces, but the straight lines on the latter do not appear as obvious.

2. Principle

The hyperbolic slit is an interesting scientific experiment where, by slowly rotating a straight rod, you can clearly see the hyperbolic slit produced when the rod passes through a curved groove. The hyperbolic slit is a mathematical method that proves the interesting situation where a tilted straight rod rotates around the Z-axis and produces a single hyperbolic surface, which is tangent to the planes perpendicular to X and Y. The straight rod can cleverly pass through it because when it rotates in a straight line, it draws a three-dimensional circle called a hyperbolic surface in the air. The line drawn along the curved edge from the top to the bottom of the hyperbolic curve is called a hyperbolic curve. The curve carved on the vertical plate is also a hyperbolic curve, which coincides with the hyperbolic curve drawn by the straight rod, so it can smoothly pass through the hyperbolic slit on the flat plate.

The surface generated by the rotation of a hyperbola around its axis of symmetry is called a hyperboloid. The appearance of a single leaf hyperboloid is very beautiful, and its stability is also relatively good. For example, the Guangzhou TV Tower, which was built to welcome the 2010 Guangzhou Asian Games, is affectionately known as the "little waist". Its main structure is a typical single leaf hyperboloid, which has left a deep impression on most Chinese and foreign visitors due to its slim and beautiful appearance. In addition, the cooling tower of thermal power plants mainly serves the cooling function of circulating water, and one of its commonly used shapes is this single blade hyperbolic surface, which has the advantages of fast convection and good heat dissipation effect.

3. Purpose

The exhibition items showcase scientific knowledge and principles of hyperbolas and single page hyperboloids in mathematics through interactive participation