3D model of a triangle with its inscribed sphere

Maths

Geometry

Points, angles and vectors, then transformations, triangles, circles and solids. Prisms, pyramids, cones and spheres become 3D models you can walk around with AR.

40 lessons
Lesson 1 free
3D
AR

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All 40 lessons

Taught with 3D models and AR.

Lesson 1Free
Basic Concepts

The building blocks of geometry, rays and line segments, and the definition of finite and infinite sets.
Lesson 2
Position report

Determination of the relative positions of spatial elements.
Lesson 3
Angles in Space

Angles between lines, planes, and lines and planes, perpendicularity, and determination of angles in space.
Lesson 4
Near and Far

Distances between points, lines and planes, units of measurement, and determination of the shortest distance.
Lesson 5
Locus in Geometry

Determination of specially positioned points and sets of points in the plane and in space.
Lesson 6
Vectors

Vectors, their magnitude and direction, opposite vectors, and the sum and difference of vectors.
Lesson 7
Planar Transformations

Basics of point transformations and congruence transformations: translation, rotation, line reflection and point reflection.
Lesson 8
Translation

Vector definition of translation and its distance-, angle- and orientation-preserving properties.
Lesson 9
Reflection

Point and line reflection, fixed points, invariant lines, and the properties of the transformations.
Lesson 10
Similarity

Similarity transformation, scale factor, reduction and enlargement, and ratios of length, area and volume.
Lesson 11
The Plane as a Mirror

Reflection about a plane, fixed and invariant shapes, and the geometric properties of a plane mirror.
Lesson 12
Rotation about a Point

Rotation about a point, direction, angle, fixed point, and identity transformations.
Lesson 13
Rotation in Space

Rotation about a line in space, rotation axis, fixed points, direction, and congruence properties.
Lesson 14
Pythagorean Theorem

Pythagorean theorem, relations between sides of right triangles, proof, and Pythagorean triples.
Lesson 15
Thales' Theorem

Thales’ theorem, its proof, inscribed angle subtended by a diameter, and applications of the theorem.
Lesson 16
Theorems about (Tri)Angles

Altitude theorem, leg theorem, intercept theorem, related proportions, and the concept of the geometric mean.
Lesson 17
Trigonometry

Trigonometric relations in right triangles: sine, cosine, tangent and cotangent functions.
Lesson 18
Laws of Sines and Cosines

Application of the laws of sines and cosines to determine sides and angles of any triangles.
Lesson 19
Quadrilaterals

Classification and properties of quadrilaterals: trapezium, parallelogram, rhombus, rectangle, deltoid and square.
Lesson 20
Outside & Inside

Properties of cyclic and tangential quadrilaterals and the related geometric theorems.
Lesson 21
Polygons

Characteristics of polygons, diagonals, interior and exterior angles, and properties of regular polygons.
Lesson 22
Polyhedra

Polyhedra, Euler’s polyhedral formula, and the characteristics of regular solids.
Lesson 23
Prisms

Definition and parts of prisms, and calculation of their surface area and volume.
Lesson 24
Right & Oblique

Comparison of right and oblique prisms, and differences in determining their surface area, height and volume.
Lesson 25
On Quadrilateral Bases

Calculation of surface area and volume of special right prisms with quadrilateral bases, with a practical example.
Lesson 26
From Column to Cube

Properties, surface area and volume of square prisms and cubes, with a practical Rubik’s Cube example.
Lesson 27
Pyramid

Definition and parts of pyramids, their derivation, right and oblique pyramids, surface area and volume formulas.
Lesson 28
Truncated Pyramid

Definition and parts of truncated pyramids, surface area and volume, and application of similarity rules.
Lesson 29
Circles

Basic circle concepts: circumference, radius, diameter, tangent, secant, chord, and calculation of circumference and area.
Lesson 30
Inside the Circle

Parts of a circle: disc, annulus, sector, segment and semicircle, and determination of their areas.
Lesson 31
Angles in the Circle

Central and inscribed angles, their corresponding arcs, and the relations between them.
Lesson 32
Spheres

Characteristics of spheres and spherical surfaces, radius, diameter, and determination of surface area and volume.
Lesson 33
Is the Earth a Sphere?

Geometric relations between the sphere and Earth, geographical coordinates, latitude and longitude.
Lesson 34
(Circular) Cylinders

Definition of cylinders, types and parts of circular cylinders, and formulas for surface area and volume.
Lesson 35
Cones

Parts of cones and cones of revolution: generator, lateral surface, base, and determination of surface area and volume.
Lesson 36
Cones of Revolution

Geometric properties of cones of revolution generated by rotating axially symmetric plane figures.
Lesson 37
Cross Sections of a Cone

Plane sections of cones of revolution: circle, ellipse, parabola and hyperbola, plus truncated-cone derivation and surface area.
Lesson 38
"Spun" around

Solids of revolution generated by rotating plane figures around a symmetry axis, and examination of their volumes.
Lesson 39
Inscribed Solids

Archimedes’ theorem, and the concept and characteristics of dual solids.
Lesson 40
A Solid in a Solid

Joined geometric solids, Platonic solids, and the stellated octahedron.