## Technical Proof Pool and Billiards Analyses

The technical proofs below contain physics background and mathematical formulas to support many of the principles in the book. Refer to the book to see how the principles are used in practice.

NOTE: this information will be of interest only to people with strong physics and mathematics backgrounds. Others proceed at your own risk.

Chapter 2 - Fundamentals

TP 2.1 - Minimum cue tip friction required for no-slip horizontal impact

Chapter 3 - Executing Basic Shots

TP 3.1 - 90° rule
TP 3.2 - Ball speeds and distances after stun-shot impact
TP 3.3 - 30° rule
TP 3.4 - Margin of error based on distance and cut angle
TP 3.5 - Effective target sizes for slow shots into a side pocket at different angles
TP 3.6 - Effective target sizes for slow shots into a corner pocket at different angles
TP 3.7 - Effective target sizes for fast shots into a side pocket at different angles
TP 3.8 - Effective target sizes for fast shots into a corner pocket at different angles
TP 3.9 - Pocket target center offsets based on angle to the pocket (see TP 3.5 through TP 3.8)
TP 3.10 - Pocket margin of error regions for a slow shot (see TP 3.5 and TP 3.6)
TP 3.11 - Pocket margin of error regions for a fast shot (see TP 3.7 and TP 3.8)
TP 3.12 - Object ball angle error based on cut angle (see TP 3.4)

Chapter 4 - Spin and English

Chapter 6 - Bank and Kick Shots

Chapter 7 - Advanced Techniques (Shot Making)

Additional proofs not referenced in the book (but referenced in Billiards Digest articles):

TP A.3 - Minimum cue elevation required for a head-spot-to-foot-spot center-ball-hit shot

TP A.14 - The effects of cut angle, speed, and spin on object ball throw