### Life of Fred

# Life of Fred High School Math Set 2 (2 books)

现在是预购期间，没有现货。8月25日发货。Life of Fred won't be shipped until Aug. 25, 2020.

This set can be started with any student who has completed Life of Fred Beginning and Advanced Algebra or has completed Algebra 2 in another curriculum. This set could also be considered a College Prep set as it prepares the student for college level maths. After completing this set, the student is ready to go into the College Set.

This set includes:

Life of Fred: Geometry (Expanded Edition) (Sample pages)

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

- Honors Problem of the century:
- 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

Life of Fred: Trigonometry (Expanded Edition) (Sample Pages)

Covers all of trigonometry including...

- Sines
- Cosines and Tangents
- Graphing
- Significant Digits
- Trig Functions of Any Angle
- Trig Identities
- Graphing a s in (bx + c)
- Radian Measurement
- Conditional Trig Equations
- Functions of Two Angles
- Oblique Triangles
- Inverse Trig Functions
- Polar Coordinates
- Polar Form of Complex Numbers
- Preview of all of Calculus