Tap tools to add shapes
Chapter 1
The Foundations
Geometry begins with simple concepts: Points (a location), Lines (straight paths), and Angles (the space between intersecting lines).
Interactive: Angles
Drag the blue point to change the angle.
Chapter 2
Triangles
A polygon with three edges and three vertices. The internal angles of a triangle always add up to exactly 180°.
Interactive: The 180° Rule
Drag any vertex to reshape the triangle.
Chapter 3
Circles & Pi
A circle is all points in a plane that are at a given distance (Radius) from a center. The magic number π (3.14159...) connects a circle's radius to its circumference and area.
Interactive: Area = πr²
Adjust the slider to change the radius.
Chapter 4
3D Space
Adding a third dimension (z-axis) gives us volume. Cubes, spheres, and cylinders exist in 3D space.
Interactive: 3D Viewer
Swipe to rotate the scene.
Coming up: Complex Polygons & The Theorem of Pythagoras!
Chapter 5
Polygons & Area
A Polygon is a closed shape with straight sides. The Area measures the surface space inside the boundary.
Interactive: Rectangle Area
Drag the corner to resize the rectangle.
Chapter 6
Pythagorean Theorem
In a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
a² + b² = c²
Interactive: Visual Proof
Drag the corner to change side lengths.
Continue to learn about Coordinates and Transformations!
Chapter 7
Coordinate Geometry
By placing shapes on a grid, we can describe geometry using numbers. The X-axis (horizontal) and Y-axis (vertical) meet at the Origin (0,0).
Interactive: Plotting & Distance
Drag the point. Geometry on a grid lets us calculate distances using the Pythagorean Theorem!
Chapter 8
Transformations
Shapes can be moved without changing their size or shape using Translation (sliding), Rotation (turning), and Reflection (flipping).
Interactive: Transform the Shape
Chapter 9
Fractal Geometry
Fractals are complex patterns that are self-similar across different scales. Zooming in reveals the same basic shape repeated forever.
Interactive: Sierpinski Gasket
Adjust the complexity level.
Wait, there is more! Gravity is actually Geometry...
Chapter 10
Gravity is Geometry
In Einstein's theory of General Relativity, gravity isn't a force, but the Curvature of Space-Time. Massive objects stretch the geometry of the universe!
Interactive: Space-Time Well
Drag the massive object to see how it curves the local geometry.
Next: Discover the Geometry hidden in Nature!
Chapter 11
Geometry in Nature
Nature is the ultimate geometer. From the Golden Spiral in seashells to the Hexagons in honeycombs, mathematics governs organic growth.
Interactive: Golden Spiral
The Fibonacci sequence (1, 1, 2, 3, 5, 8...) creates this perfect organic curve.
Chapter 12
Tessellations
A Tessellation is a pattern of shapes that fits together perfectly with no gaps and no overlaps. Regular polygons like triangles, squares, and hexagons can tile a plane forever.
Interactive: Pattern Tiling
Choose a shape to see how it fills the space.
Coming up: The fundamental branches of Geometry!
Chapter 13
Euclidean Geometry
Named after Euclid of Alexandria, this is "flat" geometry. Its most famous rule is the Parallel Postulate: through a point not on a line, exactly one parallel line can be drawn.
Interactive: Parallel Lines
Chapter 14
Non-Euclidean
In Spherical or Hyperbolic space, the Parallel Postulate fails. On a sphere, triangles have more than 180°, and parallel lines eventually meet!
Interactive: Spherical Triangle
Chapter 15
Differential Geometry
This branch uses calculus to study curves and surfaces. It measures Curvature—how much a geometric object deviates from being "flat" at any point.
Interactive: Curvature Tool
Chapter 16
Algebraic Geometry
Algebraic geometry studies shapes defined by polynomial equations. Simple examples include circles (x²+y²=r²) and complex elliptic curves.
Interactive: Equation Plotter
The Ultimate Mastery
You've finished the Absolute Geometry Masterclass.