Visualgebra

The course

One course, two strands — algebra and geometry — walked in seven chapters. Each chapter rests on the one before it, and twice they meet.

  1. 1FoundationsWhat we agree on, angles, and the first letters. Meets at distributivity as a rectangle.Point, line, ray, and segment, Angle as an amount of turning, The postulates, stated plainly, including the parallel postulate, Angles on a straight line sum to 180, Angles at a point sum to 360, Vertically opposite angles are equalGeometry & AlgebraOpen6 lessonsRests on nothing. Start here.
  2. 2StructureParallels, triangles, and equations that are consequences instead of rules.Transversals; corresponding angles, Alternate angles are equal, Co-interior angles sum to 180, The converse: equal alternate angles make lines parallel, The angle sum of a triangle is 180, The exterior angle theorem, The angle sum of any polygon, The triangle inequalityGeometry & AlgebraOpen8 lessonsRests on Foundations.
  3. 3FormCongruence, quadrilaterals, and the identities as pictures. Meets at (a+b)² as a square.What congruence means, SSS, SAS, ASA, agreed, A triangle with two equal sides has two equal angles, The converse, The perpendicular bisector is the set of points equidistant from two points, The angle bisector is the set of points equidistant from two lines, Parallelograms: opposite sides and angles equal, The diagonals of a parallelogram bisect each other, Rectangle, rhombus, square, kite, trapezium as special cases, The classification, built by the student rather than handed overGeometry & AlgebraOpen10 lessonsRests on Structure.
  4. 4AreaArea, and quadratics. Meets at completing the square, and at Pythagoras.Area of a rectangle, Half of a rectangle, Any triangle is half base times height, Area of a parallelogram, Area of a trapezium, Pythagoras, The converse of PythagorasGeometry & AlgebraOpen7 lessonsRests on Form.
  5. 5The bridgeSimilarity, and coordinates. Meets at the distance formula being Pythagoras.Similar figures; scale factor, Two equal angles are enough (AA), Corresponding sides are in constant ratio, Area scales by the square of the scale factor, The intercept theorem, The plane as pairs of numbers, Distance between two points is Pythagoras, Midpoint, Drawing a relationshipGeometry & AlgebraOpen9 lessonsRests on Area.
  6. 6RelationshipsFunctions. Meets at gradient being similar triangles.Input and outputAlgebraOpen1 lessonRests on The bridge.
  7. –7Circles and ratiosCircles, trigonometry, and systems. Meets at sin² + cos² = 1.Nothing written yet.Geometry & AlgebraNot written yet0 lessonsRests on Relationships.

Locked and not written yet are different things. A locked chapter is finished and waiting for a subscription. A chapter not written yet is on the plan and nobody can read it, including us.