(BQ) Part 2 book "Fundamentals of algebraic modeling - An introduction to mathematical modeling with algebra and statistics" has contents: Additional applications of algebraic modeling, modeling with systems of equations, probability models, modeling with statistics. | chapter five 5 Additional Applications of Algebraic Modeling IN THIS CHAPTER 5-1 Models and Patterns in Plane Geometry 5-2 Models and Patterns in Right Triangles 5-3 Models and Patterns in Art and Architecture: Perspective and Symmetry 5-4 Models and Patterns in Art, Architecture, and Nature: Scale and Proportion 5-5 Models and Patterns in Music Chapter Summary Chapter Review Problems Chapter Test Suggested Laboratory Exercises “There is no excellent beauty that hath not some strangeness in the proportion.” – Sir Francis Bacon This chapter will give you a brief taste of many areas where mathematical modeling is used every day. Several of the areas, such as music, may surprise you at first. Don’t let the fact that mathematics is involved ruin your enjoyment of music and the arts. 227 228 Chapter 5 Additional Applications of Algebraic Modeling Section 5-1 MODELS AND PATTERNS IN PLANE GEOMETRY Formulas are mathematical models that have been developed over the course of hundreds of years by mathematicians who noticed constant relationships among variables in similar problems. Many geometric formulas were developed by the Greeks and ancient Egyptians after much trial and error. Euclid, one of the most prominent mathematicians of antiquity, wrote a treatise called The Elements, which was a compilation of the geometric knowledge of the time (365–300 BC). This book was used as the core of geometry textbooks for the next 2000 years. The use of geometric formulas has made the design of buildings and construction projects much simpler. If there were no formula to calculate the area of a rectangle, for example, a person wanting to carpet a floor shaped like a rectangle would need to roll out a large sheet of paper to cover the floor, trace the outline of the floor, cut it out, take it to the store, trace it onto a piece of carpet, and cut out a suitable piece to finish the job. How much simpler it is to measure the length and width of the room and use the formula
