Heading home from the 2025 AP Calculus Reading (scoring of AP exams) in Kansas City, at the MCI airport I saw ceiling-mounted sculptures en route to terminal B that looked like they were meant for us [i]Mathy[/i] people. Okay Artsy people, you may feel free to enjoy them too — The Venn diagram overlap for these two groups is plenty spacious.[br][br]Specifically, the sculptures look like representations of 3D volumes in Calculus. The white metal (?) ribbons bridging opposite sides of the colorful base reminded me of how one learns in a Calc I class to conceptualize certain volumes as thin slices of familiar shapes. We develop a strategy to compute the volumes of the many individual slices, and then we sum that list of numbers to find the total volume. Photos of the sculptures follow the GeoGebra construction immediately below.[br][br]The GeoGebra construction is inspired by the Kansas City airport sculptures. I wanted the base in the x-y plane to be a smooth, closed curve with a number of swerves. I thought of letting the sliders be a mystery and letting the user figure out what they do through experimentation. However, the performance of this construction is not nearly as responsive as I would have liked, so I'll at least offer that each half of the border is a sum of:[br][list][*][math]y=a\sqrt{R^2-x^2}[/math], semicircle with radius [b][color=#1e84cc]R[/color][/b] that is stretched/shrunk in the y-direction by a factor of [b][color=#1e84cc]a[/color][/b].[/*][*][math]y=b\cdot sin\left(c\left(x-d\right)\right)[/math], sinusoid with amplitude [b][color=#1e84cc]b[/color][/b], horizontal stretch/shrink coefficient [b][color=#1e84cc]c[/color][/b], phase shift [b][color=#1e84cc]d[/color][/b].[/*][*]A line that ensures that each half will begin and end on the x-axis.[/*][/list]Furthermore, the additional two black sliders offer:[br][list][*]vertical shrink/stretch factor [b][color=#1e84cc]h[/color][/b] of the parabolic ribbons/slices in the z-direction.[/*][*]number of slices [b][color=#1e84cc]n[/color][/b].[/*][/list][br]GeoGebra controls:[br][list][*]In left graphics region, the sliders, checkbox, input boxes, and buttons are mostly self-evident.[/*][*][b]Because of the slow responsiveness, typing values into the input boxes may work better on your device than using the sliders.[/b][/*][*]For finer control of sliders with a mouse & keyboard, click on a slider and use arrow keys to adjust in small increments. Pressing shift/control key along with the arrow keys will adjust in smaller/larger increments.[/*][*]On keyboard, use Tab key to jump from one control to the next. Shift-Tab jumps backwards through the controls.[/*][*]In right 3D graphics region, alter the 3D perspective by click/dragging with mouse or using typical touchscreen gestures.[/*][*]In right 3D graphics region, hold Shift and then click/drag to pan within the x-y plane. Hold Shift and then click (without dragging) to toggle mode, after which Shift and then click/drag will pan in the z-direction.[/*][/list]