## 18.1 Outline

1. What is Calculus?
1. Calculus is the mathematics of motion and change.
2. The three main ideas of calculus are limit, derivative, and integral
2. The Limit: Zeno’s Paradox
1. Achilles and the tortoise
2. limit of a sequence
3. The derivative: the tangent
See the whole entry “Section 18.1: What is Calculus?”

## Homework Hints 15-4

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 … See the whole entry “Homework Hints 15-4”

## 15.4 Outline

1. Introduction
1. definition
2. model
2. Geometric definition of conic sections
1. parabola
1. focus
2. directrix
3. axis
4. vertex
2. ellipse
1. foci
2. major axis
3. center
4. minor axis
3. circle
1. center
4. hyperbola
1. transverse axis
2. center
3. conjugate axis
3. Algebraic definition of conic sections
1. general form
1. first-degree equation
See the whole entry “Section 15.4: Conic Sections”

## Homework Hints 8-2

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 … See the whole entry “Homework Hints 8-2”

## 8.2 Outline

1. Rectangles
1. define area
2. define square unit
3. formulas
1. rectangle
2. square
2. Parallelograms
1. definition
2. formula
3. derivation of formula
3. Triangles
1. formula
2. derivation of formula
4. Trapezoids
1. definition
2. formula
3. derivation of formula
5. Circles
1. formula
2. derivation of formula
6. Applications
1. conversion application
2. acre definition
3. conversion of
See the whole entry “Section 8.2: Area”

## 7.6 Outline

1. Golden rectangles
1. definition
2. divine proportion
3. tau
2. Mathematics and art
1. golden ratios in art
2. proportions of the human body
3. spiral constructed using a golden rectangle
3. Projective geometry
1. Duccio’s Last Supper
2. Hogarth’s Perspective Absurdities
3. false perspective
4. Masaccio’s The Holy Trinity
See the whole entry “Section 7.6: Mathematics, Art, and Non-Euclidean Geometries”