Which modes are included?

Coordinates (distance, midpoint, slope), irregular polygon area, protractor angle, unit-circle trig, and Fourier epicycles with sine, square, and sawtooth presets.

How do I add polygon vertices?

Select Polygon mode, turn on Add vertices, then click the grid (up to 12 points). Leave Add vertices off to orbit or drag numbered handles. Undo point removes the last vertex; Reset restores the starter quad.

How do handle drags work on the 3D stage?

Hover a colored handle until the cursor shows grab, then drag. Movement follows the ground plane under your pointer, and orbit is paused until you release.

Why does orbit stop when I drag a point?

Orbit controls are paused during handle drags so the camera does not fight the edit. Release the handle to orbit again.

What is the shoelace formula?

It computes polygon area from vertex coordinates by summing cross products around the boundary. Plot Lab shows the absolute area.

Can I enter exact coordinates numerically?

This version is drag-first on the 3D grid. Use the live readouts to note values, or zoom in for finer placement.

What does the Fourier mode show?

It builds a waveform as a sum of rotating vectors (epicycles). The right-hand curve is the partial sum of a_n sin(n t). Presets load classic coefficients; drag the n= handles to change amplitudes.

Plot Lab

Explore coordinate geometry on a live 3D stage. Drag points for distance, midpoint, and slope; click a polygon together; measure angles; walk the unit circle; or build waveforms with Fourier epicycles.

Orbit the grid, pause rotation while handles are held, and read metrics as the diagram updates. Built for intuition first, formulas second.

Geometry & Math

Plot Lab

Interactive coordinate geometry on a live 3D stage: plot points, build irregular polygons, measure angles, explore the unit circle, and watch Fourier epicycles build a waveform.

Distance

4.25

Midpoint

(0.35, 0.55)

Slope

0.568

Δx, Δy

3.7, 2.1

Tip: grab a colored handle (cursor becomes grab), then drag freely across the grid. Orbit pauses while you hold a handle. In Polygon mode, turn on Add vertices before clicking the grid. In Fourier mode, use presets and drag harmonic amplitudes while the epicycles spin.

About Plot Lab

What this tool does

Plot Lab is an interactive 3D geometry studio for coordinate points, irregular polygons, protractor angles, unit-circle trigonometry, and Fourier-series epicycles.

You drag handles on a grid stage while distance, midpoint, slope, shoelace area, degrees/radians, sin/cos/tan, and harmonic amplitudes update live.

Static worksheets can list the same formulas. This tool is built for motion: orbit the scene, reshape a figure, and watch the metrics track the diagram.

Everything runs in your browser. Plot units are abstract; treat them as any consistent length unit.

How to use it

1Choose a mode: Coordinates, Polygon, Protractor, Unit circle, or Fourier.
2Drag the colored handles on the grid. Orbit pauses while a handle is held.
3In Polygon mode, turn on Add vertices before clicking the grid; use Undo point or Reset as needed.
4Read the stats row for distance, area, angles, trig values, or harmonic amplitudes.
5For the unit circle, drag point P around the circle to change θ.
6For Fourier, pick a sine, square, or saw preset, then drag n= handles to change amplitudes while epicycles spin.
7Switch modes anytime; each mode keeps its own working state in the session.

Practical tips

Coordinates mode draws rise and run guides so slope is visible, not only printed.
Polygon area uses the shoelace formula; self-intersecting shapes can look odd, so keep vertices in order around the boundary.
Protractor rays meet at the origin; the highlighted wedge is the smaller angle between them.
Near cos θ = 0, tangent grows without bound; the readout shows infinity when the line is vertical.
Fourier square waves use odd harmonics; sawtooth uses n = 1, 2, 3, 4. Zero an amplitude to drop that term.

Frequently asked questions

Which modes are included?: Coordinates (distance, midpoint, slope), irregular polygon area, protractor angle, unit-circle trig, and Fourier epicycles with sine, square, and sawtooth presets.
How do I add polygon vertices?: Select Polygon mode, turn on Add vertices, then click the grid (up to 12 points). Leave Add vertices off to orbit or drag numbered handles. Undo point removes the last vertex; Reset restores the starter quad.
How do handle drags work on the 3D stage?: Hover a colored handle until the cursor shows grab, then drag. Movement follows the ground plane under your pointer, and orbit is paused until you release.
Why does orbit stop when I drag a point?: Orbit controls are paused during handle drags so the camera does not fight the edit. Release the handle to orbit again.
What is the shoelace formula?: It computes polygon area from vertex coordinates by summing cross products around the boundary. Plot Lab shows the absolute area.
Can I enter exact coordinates numerically?: This version is drag-first on the 3D grid. Use the live readouts to note values, or zoom in for finer placement.
What does the Fourier mode show?: It builds a waveform as a sum of rotating vectors (epicycles). The right-hand curve is the partial sum of a_n sin(n t). Presets load classic coefficients; drag the n= handles to change amplitudes.

Plot Lab

Plot Lab

About Plot Lab

What this tool does

How to use it

Practical tips

Frequently asked questions

More reading

Plot Lab

Plot Lab

About Plot Lab

What this tool does

How to use it

Practical tips

Frequently asked questions

More reading