## Life of Fred Mathematics

### Life of Fred: Geometry

One day in Fred's life in which he . . .

• Falls in Love!

• Teaches you how to write an opera!

• Buys Hecks Kitchen!

• Does all of geometry up to the 14th dimension!

Geometry is one course that is different from all the rest. In the other courses, the emphasis is on calculating, manipulating and computing answers. In contrast, in geometry there are proofs to be created. It is much more like solving puzzles than grinding out numerical answers. For example, if you start out with a triangle that has two sides of equal length, you are asked to show that it has two angles that have the same size.

You will need at least one year of high school algebra. (Life of Fred: Beginning Algebra). In this geometry book for example, on p. 26 we will go from y + y = z to y = ½ z. It is preferable, however, that you have completed the two years of high school algebra. (Life of Fred: Beginning Algebra and Life of Fred: Advanced Algebra Expanded Edition). Most schools stick geometry between the two years of algebra – beginning algebra, geometry, advanced algebra – but there are a couple of reasons why this is not the best approach.

First, when you stick geometry between the two algebra courses, you will have a whole year to forget beginning algebra. Taking advanced algebra right after beginning algebra keeps the algebra fresh.

Second, the heart of geometry is learning how to do proofs. This requires an "older mind" than the mechanical stuff in the algebra courses. A person's brain develops in stages. Most three-year-olds don't enjoy quiz shows on television.

- 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

Unlike all other math programs, this one also has:

• The only verse of Fred's famous song, "Another Day, Another Ray"

• The difference between iambic, trochaic, anapestic and dactyllic in poetry

• How easy it is to confuse asinorum which is in the genitive plural in Latin with asinus which is in the nominative singular.

• A good use for Prof. Eldwood's Introduction to the Poetry of Armenia while on the deck of a pirate ship

All answers are included in the textbook.

Click here to view a sample lesson (Opens in a new window or tab)

Life of Fred Geometry is a hardcover textbook containing 560 pages. This book is not consumable. All answers are written on separate paper or in a notebook.

Number of Lessons: 2 Semesters, Thirteen regular chapters and six bonus honors chapters. Expect to take anywhere from 9 to 14 months to complete. The amount of time required will be determined by the number of optional chapters (such as 5 1/2 and 7 1/2) you choose to cover and the academic ability of the student. Recommendation: Have the student look at the table of contents and plan out a schedule that will have the book completed in about a year. Taking responsibility for their own education is an important skill to learn.