Overview

This captivating 'Life of Fred' math book is part of an innovative series that seamlessly weaves math concepts into an engaging narrative, following the journey of a character named Fred. These books make learning math an enjoyable adventure, fostering deep understanding and a lifelong love for the subject.

In this course you will learn about...

  • Non-Euclidean Geometry
    • Attempts to prove the Parallel Postulate
    • Nicolai Ivanovich Lobachevsky's geometry
    • Consistent Mathematical theories
    • Georg Friedrich Bernhard Riemann's geometry
    • Geometries with only three points
  • Points and Lines
    • Attempts to prove the parallel postulate
    • Collinear points
    • Concurrent lines
    • Coplanar lines
    • Coordinates of a point
    • Definition of when one point is between two other points
    • Exterior Angles
    • Indirect Lines
    • Line segments
    • Midpoint
    • Parallel lines
    • Perpendicular Lines
    • Perpendicular Bisectors
    • Postulates and theorems
    • Skew lines
    • Distance from a point to a Line
    • Tangent and secant lines
    • Theorems, propositions, lemmas, and corollaries
    • Undefined terms
  • Quadrilaterals
    • Honors Problem of the century:
      If two angle bisectors are congruent
      when drawn to the opposite sides,
      then the triangle is isosceles
    • Intercepted segment
    • Kite
    • Midsegment of a triangle
    • Parallelogram
    • Rectangle
    • Rhombus
    • Square
    • Trapezoid
  • Solid Geometry
    • Euler's theorem
    • A line perpendicular to a plane
    • Distance from a point to a plane
    • Parallel and perpendicular planes
    • Polyhedrons
      • hexahedron (cube)
      • tetrahedron
      • Octahedron
      • Icosahedron
      • Dodecahderon
    • Volume Formulas: cylinders, prisms,
      cones, pyramids, spheres
    • Cavalieri's Principle
    • Lateral Surface Area
  • Symbolic Logic
    • Contrapositives
    • If...then...statements
    • Truth tables
  • Triangles
    • Acute and Obtuse Triangles
    • Adjacent, opposite, hypotenuse
    • Altitudes
    • Angle bisector theorem
    • Definition of a triangle
    • Drawing auxiliary lines
    • equilateral and equiangular triangles
    • Hypotenuse-leg theorem
    • Isosceles triangle theorem
    • Medians
    • Pons Asinorum
    • Proof that a right angle is congruent
      to an obtuse angle using euclidean geometry
    • Proportions
    • Right Triangles
    • Scalene Triangles
    • Similar triangles
    • SSS, SAS, ASA postulates
    • Angles
      • Acute, obtuse, and right angles
      • Alternate interior angles and corresponding angles
      • Congruent angles
      • Degrees, minutes, and seconds
      • Euclid's The Elements
      • Exterior angles
      • Inscribed angle theorem
      • Linear pairs
      • Rays
      • Supplementary angles
      • Two proofs of the exterior angle theorem
      • Vertical angles
    • Area
      • Area and volume formulas
      • Heron's Formula
      • Parallelograms
      • Perimeter
      • Polygons
      • Pythagorean Theorem
      • Rectangles, Rhombuses, and Squares
      • Trapezoids
      • Triangle inequality
      • Triangles
    • Circles
      • Center, radius, chord, diameter, secant, tangent
      • Concentric circles
      • Central Angles
      • Circumference
      • Arcs
      • Inscribed angles
      • Proof by Cases
      • Sectors
    • Constructions
      • Compass and straightedge
      • Rules of the Game
      • Rusty compass constructions
      • Golden Rectangles and golden ratio
      • Trisecting an angle and squaring a circle
      • Incenter and circumcenter of a triangle
      • Collapsible compass constructions
      • 46 popular constructions
    • Coordinate Geometry
      • Analytic geometry
      • Cartesian/rectangular/orthogonal coordinate system
      • Axes, origins, and quadrants
      • slope
      • distance formula
      • midpoint formula
      • proofs using analytic geometry
    • Flawless (Modern) Geometry
      • Proof that every triangle is isosceles
      • Proof that an obtuse angle is congruent to a right angle
      • 19-year-old Robert L Moore's modern geometry
    • Geometry in Dimensions
      • Geometry in Four Dimensions
      • Geometry in high dimensions
      • Complete chart up to the 14th dimension
      • Stereochemistry and homochirality
      • Five manipulations of proportions
      • tesseracts and hypertesseracts
    • Polygons
      • Definition of a polygon
      • Golden rectangles
    • Proofs
      • Proof of a theorem in paragraph form
      • Hypothesis and conclusion
      • Indirect proofs
      • Hunch, hypothesis, theory, and law
      • Proofs of all the area formulas given
        only the area of a square (This is hard.
        Most books start with the area of
        a triangle as given.)
      • Proofs of the Pythagorean theorem
      • Definition of a limit of a function
      • Inductive and deductive reasoning
      • Proofs using geometry

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