Perfect Design

Using Mathematics and Geometry to Build Great Landscape Designs: How to Forever Think Differently about Visual Design

Richard G. Starshak

• Publisher: Christian Faith Publishing, Inc.
• Year: 2022
• Print ISBN: 9781638441762
• eBook ISBN: 9781638441779
• Topic: Sciences biologiques
• Subtopic: Horticulture

Designing by mathematics (numbers, order, quantities, and measures) and geometry (points, lines, angles, and shapes) is a totally different approach to create any and all visual design! The combination of these two related, but very different areas, form the foundation of perfect visual design. We will show in detail how to use simple mathematics and geometry to create perfect order, balance, and emphasis in the landscape design!

Chapter 1

Mathematical Beginnings

Mathematics and geometry surround us with fascination as they should and from the earliest times of recorded history. Even in the earliest records, we see counting and measuring (Samaria 3100 BC), a ten-number mathematical system in use (Egypt 2700 BC), geometric tables established with mathematical problems noted (Samaria 2600 BC), fractions and algebraic equations (Babylon 1700 BC), and a decimal numbering system with place value in practice (China 1200 BC).

We can look far back in the historical records and find among many things writings about squares and rectangles, the illusive problem of the square root of two (India 800–400 BC), and the use of rows and columns (China 700–600 BC). The Greeks and their far-reaching quest for wisdom contributed a large volume of mathematical and geometric knowledge. With the Greeks and their culture, the world gained the insights of a vast array of mathematicians, philosophers, composers, and astronomers.

We see incredible mathematical contributions from Greece over a few hundred years with the following:

Thales (624–546 BC)	Theories and triangles
Pythagoras (570–495 BC)	Geometric squares and triangles
Hippasus (500 BC)	Irrational numbers
Zeno of Elea (490–430 BC)	Infinity
Hippocrates (470–410 BC)	Summarized past principles
Democritus (460–370 BC)	Fractions, columns, and cone shapes
Plato (428–318 BC)	Platonic solids, geometric proofs
Aristotle (384–322 BC)	Logic and mathematical reasoning
Euclid (300 BC)	Proofs, postulates, and axioms
Archimedes (287–212 BC)	Shapes, infinites, and value of pi

Figure 1-1 Mathematical contributions from Greece

With knowledge deepening, we see one generation building upon the previous generation, adding pieces of knowledge, expanding on what has been discovered, and stepping into the new frontiers of how mathematics and geometry reveal the design construction of the world around us. There is so much foundation, structure, and possibilities found in the numbers around us that every generation, from time long ago until today, shares in the excitement of new discoveries.

Finding the relationship between the diameter and the circumference of a circle or discovering the formula of finding the length of the far leg of a right triangle probably gave as much excitement as Fibonacci’s writings of the sequence such named after him (1200s); factoring, trigonometry, and analysis of pi (1300s); trigonomic functions (1400s); natural logarithms, Luca Pacioli’s Divine Proportion and imaginary numbers (1500s); analytical geometry and John Wallace’s development of calculus (1600s); Newton’s infinitesimal calculus and infinite powers (1700s); descriptive geometry, probability, quadratic reciprocity, prime numbers, least squares analysis, hyperbolic geometry, and elliptical functions (1800s); sets, graphs, probability, differential geometry, geometric topology and a myriad of mathematical truisms, proofs, and ah-ha moments (1900s); and a never-ending list of ever expanding theories, revelations, proofs, and applications (2000s)!

Our fascination is heightened when we can see application of such principles. As far back as 2725 BC and the construction of the Great Pyramid, we can observe various angles, ratios, and measurements. Although a multitude of conclusions have been drawn over time about the construction, some commentaries for and against such knowledge and application, it would be indeed difficult to argue against all such geometric applications being of just chance and lacking a knowledgeable basis in such a major construction.

We see that the ancient cultures of Egypt, Greece, India, China, and throughout the Middle East used geometric principle in the design and construction of various buildings, temples, and mosques as well as in other ornate artifacts in which to adorn them.

It would be difficult to imagine a culture not utilizing even the simplest of geometric principles to divide and lay...

Table of contents

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11
• Chapter 12