Tag Archives: Math

Kerning and Hyperbolic Paraboloids

kern-type-the-kerning-game-RS

A friend sent me a link to an online kerning game, and I think I might have found my true calling, lulz. I guess my sphere of OCDity extends to include the spacing of letters, even though I’m not a visual person. Arranging and organizing images I can see before me = system running, conceptualizing or manipulating visualizations = system overload. Like I’m truly in awe of people who are good with maps, people who know which direction they’re traveling when they make turns without having to pause and think and confuse themselves in the process.

To segue into math, hyperbolic paraboloids are pretty trippy quadratic surfaces. I know what a hyperbolic paraboloid looks like and I can graph one,1 but mentally rotating it (interchanging x, y, and z variables), visualizing traces in various coordinates planes, changing the coefficients, shifting the vertex or attempting to extend 2-D conics in 3-D space, results in the aforementioned system overload crashes.

Hyperbolic Paraboloid Rotation

Hyperbolic Paraboloids Rotation 1

Hyperbolic Paraboloids Rotation 2

Hyperbolic Paraboloid Flipping: c > 0, c < 0

hyperbolic paraboloid positive c, negative c, flipping

Critical Point: Saddle Point (Neither Relative Maxima Nor Relative Minima)

hyperbolic paraboloid saddle point

Vertical traces (cross sections) are parabolas; horizontal traces are hyperbolas.

Hyperbolic Paraboloid Hyperbola Trace Gif

Did You Know?

Saddles and pringles are hyperbolic paraboloids.

Hyperbolic Paraboloid Saddles Pringles

Notes

1 Well, admittedly by lazily renaming the x, y, z-axes, yes.

Sources

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