During my visit to score AP® Calculus exams in Kansas City (2023), each day I stopped to admire the sculpture hanging from the lobby ceiling of the Sheraton Hotel. Numerous other patterned geometric elements in the vicinity caught my attention too, but the sculpture was by far the most eye-catching.[br][br]A curious passerby must wonder: [br][i]How many of those metal spheres are used in the sculpture[/i]?[br][br]From the photo, how would you go about answering that question? Brute-force counting? Elegant (or not) algebra? Geometry principles? Technological assistance or not?[br][br]How would you generalize your process to account for larger or smaller iterations of this sculpture (with more or less layers of spheres)?[br][br]Does the GeoGebra construction below help in your exploration?

If you're not already familiar with GeoGebra:[br]Click the ⛶ icon in the lower/right of the graphics view to fill the screen.[br]In addition to pressing the ▶︎ button, you may change your viewing perspective in the graphics view by dragging/scrolling with a mouse or swiping/pinching on a touchscreen.