# Life of Fred Geometry Expanded

**Description**

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.

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

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.