quadratic seascape polypad

Build a Coast From Parabolas

Move a slider and redraw the coast, data, probability, and geometry.
Draggable quadratic controls for the generated coastsun vertexwave controlshore vertexcloud dome
2D view | seed 4412morning coastanimated parabolas | 8/28 buoys above threshold
wave cresty = -0.38(x - h)^2 + k
cloud domey = -0.52(x - h)^2 + k
shoreliney = 0.08(x - h)^2 + k
buoy sample dot plot
Each buoy is one wave-height data point generated from the quadratic sea.Dot plot of virtual buoy wave heights0510event threshold
probability event
P(height ≥ 6.4) = 8/28
29%

Adjust wave curvature, wind, or tide to see the event probability change in real time.

sample statistics
n28
mean5.5
median5.7
max7.6

Cloud cover becomes a second probability model: P(cloudy sky) = 58%.

categorical distribution
Calm
6
Rolling
19
Surge
3
Amplify Probability + DataCompare two coast settings and argue which one has the stronger evidence for a surge-heavy day.

Students can use counts, proportions, mean, median, and the live dot plot to support a claim from the same visual model.

Amplify Geometry + 3D

Turn the coast into measurable shapes.

The 2D sail triangle becomes a 3D triangular prism, buoy data becomes a cylinder, and the shoreline curve becomes an approximated arc length.

Geometry sketch of the sail and shoreline measurementsbase 5.2height 7.355 degprism deptharea 18.7 sq u
sail area18.7 sq u
sail perimeter21.3 u
mast angle55 deg
shore arc10.02 u
sail prism volume13.3 cu u
buoy cylinder volume7.4 cu u
geometry investigationWhich measurement changes fastest when you raise wave curvature: shoreline arc length, sail volume, or buoy volume?

Use the live measurements to make a claim, then support it with a comparison of two different coast settings.

cloud systemClouds are stitched from drifting downward-opening quadratic Bézier domes.

The cloud slider changes how many parabolic domes appear, while motion lets the sky breathe.

wave fieldWaves are animated stacks of quadratic arcs, each with its own vertex and width.

Higher curvature pulls the control point upward, making sharper crests, moving foam, and a livelier shore.

art promptFreeze the motion, drag a handle, then play it again.

Explain how changing a vertex or control point changes the feeling of the coast.

classroom connectionStudents manipulate quadratic curvature, vertices, and translations to create a coastal artwork.
wave: y = a(x - h)^2 + kcloud dome: quadraticCurveTo(control, end)shoreline: two joined quadratic arcs