Table of Contents

• Prequiz...
• The Power Function
• 1: Introduction
• 2: What are scaling relationships?
• 3: The power function
• 4: The shape of the power function
• 5: The conversion factor "a"
• 6: The power factor "b"
• Log Transformations
• 7: Introduction
• 8: What are logarithms again?
• 9: Graphing on a log scale
• 10: Visualizing the data
• 11: Getting to a straight line
• 12: The key parameter is "b"
• The value of "b"
• 13: Introduction
• 14: A geometric approach
• 15: Scaling surface area of cubes
• 16: Scaling surface area of cubes
• 17: A "2/3 scaling law"?
• Confronting ideas with data
• 18: Introduction
• 19: An unexpected result
• 20: A "3/4 scaling law"?
• 21: Internal transport systems
• 22: Branching and supply networks
• 23: Deriving the "3/4 scaling law"
• 24: So what's the real value of "b"?
• Review
• 25: Review of Concepts

Confronting ideas with data

In this section, we explore the very current controversy about the nature of the scaling relationship between body size and metabolism. In one corner, we have a group that has offered a rather complicated explanation about why there is a 3/4 power relationship. In the other corner, we have a group that says you still can't rule out the 2/3 power relationship.

Warning: there are no answers at the end of this section - because this controversy is still an active one (and probably will be for a long time). However, its impossible to even begin to understand the controversy without understanding the math behind it all. So we hope that you come away from this module with that basic understanding.