Padovan, Pascal and Proofs Without Words

Please join the Math Dept for a talk by David Nacin of William Paterson University.

This is a general audience talk. Anyone with an appreciation for beautiful patterns is encouraged to attend!

 

 

 


Oct22
12:00 pm
2020-10-22 12:00:00 2020-10-22 12:00:00 Padovan, Pascal and Proofs Without Words

What happens when we attempt to construct the Fibonacci spiral with triangles instead of squares? We get a new sequence, the Padovan sequence, which answers its own collection of unique and beautiful counting problems. In this talk we will show how this construction defines this sequence and then rediscover the same sequence hiding again in other surprising places. We then prove several identities without using either words or numbers, by considering triangles composed of colored dots.

The Fibonacci sequence is connected to the golden ratio which arises from a simple question about rectangles and proportion. A slightly different natural question leads to a new ratio and yet another method for defining our sequence. We then observe the uses of this sequence and its ratio in architecture and discuss the history behind the patterns we've uncovered. We conclude with a counterexample to a conjecture about this sequence that leads us to a final construction involving copies of the Fibonacci sequence itself.

David Nacin is the author of Math-Infused Sudoku: Puzzle Variants at All Levels of Difficulty
 

Talk is sponsored by Remsen Bird.

 

Zoom Info:

https://occidental.zoom.us/j/86954496054

Meeting ID: 869 5449 6054

Passcode: 8675309

 

America/Los_Angeles public
Event Date: Thursday, October 22, 2020

What happens when we attempt to construct the Fibonacci spiral with triangles instead of squares? We get a new sequence, the Padovan sequence, which answers its own collection of unique and beautiful counting problems. In this talk we will show how this construction defines this sequence and then rediscover the same sequence hiding again in other surprising places. We then prove several identities without using either words or numbers, by considering triangles composed of colored dots.

The Fibonacci sequence is connected to the golden ratio which arises from a simple question about rectangles and proportion. A slightly different natural question leads to a new ratio and yet another method for defining our sequence. We then observe the uses of this sequence and its ratio in architecture and discuss the history behind the patterns we've uncovered. We conclude with a counterexample to a conjecture about this sequence that leads us to a final construction involving copies of the Fibonacci sequence itself.

David Nacin is the author of Math-Infused Sudoku: Puzzle Variants at All Levels of Difficulty
 

Talk is sponsored by Remsen Bird.

 

Zoom Info:

https://occidental.zoom.us/j/86954496054

Meeting ID: 869 5449 6054

Passcode: 8675309

 

Sponsored by: Mathematics
David Nacin Talk