curvat.io — Visual Geometry & Dynamic Calculus

Pythagoras

Curvat.io

kur·vaht·eee·oh • Latin: “it curves”

Visual Geometry & Dynamic Calculus

“Think in curves.”

Curvat.io is an open visual calculus laboratory and dynamic geometry workspace designed for focused classroom exploration. Explore mathematical relationships with smooth 60 FPS numerical calculus, native implicit curve solving, real-time LaTeX editing, dynamic secant-to-tangent gliders, and responsive mobile-first graphing—all without accounts or tracking.

Classical Roots & Visual Mathematics

Named from the classical Latin curvat (“it curves, bends, or arches”), the platform bridges classical geometric intuition—from Pythagorean proportions and Euclidean constructions—to modern dynamic calculus.

Origins & EduNetSystems

Curvat.io is built and powered by EduNetSystems as an open visual learning tool for mathematics education.

Core Technologies:

JSXGraph (Canvas & SVG)
MathLive & KaTeX
MathJS CAS Engine

Architecture:

Pure ES6+ Native Modules
Zero Bundlers / Build Steps
Client-Side Computing & Privacy

Privacy, Compliance & Institutional Trust

No accounts required. All calculations run locally in your browser. Graph data is stored in the shared link or local graph file. In LMS embeds, analytics are automatically disabled for strict FERPA and COPPA compliance.

Privacy Notice • Accessibility • Terms & License

curvat.io is an interactive visual calculus laboratory built for dynamic mathematics education. Think in curves.

Calculus Suite

Points on Curve: Add dynamic gliders directly on any function curve \(y = f(x)\). Connect them with line(AP) or segment(AP) (where \(P\) is the tangent glider) to demonstrate secant lines converging into tangent lines!
Tangent Line \(f'(c)\) & Slope Triangle: Attaches a draggable glider point of tangency \(P\). Toggle \(\Delta y / \Delta x\) to attach an interactive slope triangle showing rise, run, and numerical rate of change.
Derivatives \(f', f''\): Plots the first and second numerical derivative curves dynamically.
Definite Integral \(\int_a^b f\): Shaded region with draggable boundary points \(a\) and \(b\).
Riemann Sums \(\sum f\): Interactive partition rectangles with 6 rules (Left, Right, Midpoint, Trapezoid, Lower, Upper) and dynamic \(n\) slider.

Supported Mathematical Expressions

Category	Example Syntax	Description
Function	`x^3 - 3*x` or `y = sin(x)`	Explicit function in \(x\)
Domain Restriction	`y = 2x {x < 0}` or `y = x^2 {-2 <= x <= 2}`	Restrict curve domain using curly braces with single or chained inequalities
Piecewise Function	`{x < 0: 2x, 2}` or `{x < -1: -1, -1 <= x <= 1: x, 1}`	Piecewise defined functions with conditions, branch expressions, and default fallback
Polar Curve	`r = 3sin(4theta)` or `r = 2 + 2*cos(theta)`	Polar equation in \(r\) and \(\theta\) (roses, cardioids, spirals)
Parametric Curve	`(3cos(3t), 2sin(4t))` or `x = cos(t), y = sin(t)`	Planar curve in parameter \(t\) with animated tracing and domain controls
Differential Eq	`dy/dx = x - y` or `slopefield(x - y)`	Dynamic slope field / direction field grid
Implicit Curve	`x^2 + y^2 = 25`	Conic circle, ellipse, or hyperbola
Vertical Line	`x = 2.5`	Draggable vertical line (VLT)
Point & Point Lists	`(2, 3)`, `(3, 4), (2, 1)`, or `A = (1, 4), B = (3, 2)`	Single or multiple points in one card; auto-labeled \(A, B, D\dots\) or custom labels; individually draggable
Segment	`segment(A, B)` or `segment(AB)`	Line segment between points; dynamically updates when dragged
Line	`line(A, B)` or `line(AB)`	Infinite line passing through two points
Ray	`ray(A, B)` or `ray(AB)`	Ray starting at \(A\) passing through \(B\)
Midpoint	`midpoint(A, B)` or `midpoint(AB)`	Dynamic midpoint between \(A\) and \(B\)
Circle	`circle(A, B)` or `circle(A, 3)`	Circle with center \(A\) through point \(B\) or with radius \(r\)
Polygon	`triangle(A, B, C)` or `polygon(ABCD)`	Shaded 2D polygon with vertices
Direct Coordinates	`segment((1, 2), (3, 4))`	Geometric constructs with coordinate pairs directly
Interpolation	`lagrange ABCD`	Lagrange polynomial through points

Shortcuts & Workflow

Enter Key: Press Enter in any expression card to immediately create and focus a new card.
Text Shortcuts: Type sqrt, segment, line, ray, circle, sin, cos to auto-expand interactive math templates.
Dynamic Geometry: Dragging points on the canvas dynamically updates connected segments, lines, and polygons in real time!

About & Trust

curvat.io is an open visual mathematics and dynamic calculus platform developed in partnership with EduNetSystems. Think in curves.

Privacy Notice (FERPA/COPPA) • Accessibility (WCAG 2.1 AA) • Terms & License