GE141 - Course Introduction

Graphics and Algebra

Dr Robert Batzinger
Instructor Emeritus

2/27/23

1 Application of Proportions

2 Size of Plants

  • Tall trees have smaller, dryer leaves which are less efficient at photosynthesis.
  • The weight of a tree at the root proprotional to its height
  • The taller trees requires greater area from which to draw water and minerals
  • A tall tree requires a very long lifespan.

3 Size of Warm blooded Animals

3.1 Bird size

3.2 Evolution summary

Big is Good

  • better defense
  • faster speed
  • longer endurance
  • better thermal insultation
  • more efficient energy handling

Size has drawbacks

  • Fewer opportunities to shelter
  • Larger energy consumption
  • In ability to fly
  • Weight creates pressure and growth limits

4 Age adjusted photography

4.1 Normal growth

## Body proportion

4.2 Arm to height ratios

5 Empire State Building, New York

  • 7,366 square meter foot print

  • 365,000 megatons (metric)

  • 250,000 square m of office space

  • 13,500 people working in the building, 20,000 visitors / day

  • 380 m tall (443 m with the spire and radio tower)

  • 73 elevators, 20 - visitor express 103 stories in 30 seconds: (tickets $47-$87)

5.1 Empire State Building Run up

5.2 Size of Buildings

5.3 Breaking point

  • Stone will break under a pressure of 4.2-16.7 megaton/m^2

  • Steel beam break under a pressure of 60-150 megaton/m^2

  • Weight of water is 100 kg / m^2 for each 10 cm of height ( 1kg/m^2 = 0.0014 pound /in^2)

6 Photoscaling

An artist wanted to show that the disposable income of worker in the U.S. is twice that of a worker in France. He draws one car for the French worker and “twice as large”—for the American. Evaluate the validity of the graphic he developed.

6.1 Scaled graphic

PYU GE141 2022/1: GE 141 Mathematics for daily life [4]