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BEGIN:VEVENT
UID:0f5b32bcff252fbc634dd172427d7b5f
CATEGORIES:Experimental Mathematics Seminar
CREATED:20210215T102308
SUMMARY:Padovan, Pascal, and Proofs without Words
LOCATION:zoom
DESCRIPTION:Abstract: What happens when we attempt to construct the Fibonacci spiral wi
 th triangles instead of squares? We get a new sequence, the Padovan sequenc
 e, which answers its own collection of unique and beautiful counting proble
 ms. In this talk we will show how this construction defines this sequence a
 nd then rediscover the same sequence hiding again in other surprising place
 s. We then prove several identities without using either words or numbers, 
 by considering triangles composed of colored dots.\nThe 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 observ
 e the uses of this sequence and its ratio in architecture and discuss the h
 istory behind the patterns we've uncovered. We conclude with a counterexamp
 le to a conjecture about this sequence that leads us to a final constructio
 n involving copies of the Fibonacci sequence itself.\n
X-ALT-DESC;FMTTYPE=text/html:<p><i>Abstract</i>: What happens when we attempt to construct the Fibonacci
  spiral with triangles instead of squares? We get a new sequence, the Padov
 an sequence, which answers its own collection of unique and beautiful count
 ing problems. In this talk we will show how this construction defines this 
 sequence and then rediscover the same sequence hiding again in other surpri
 sing places. We then prove several identities without using either words or
  numbers, by considering triangles composed of colored dots.</p><p>The Fibo
 nacci sequence is connected to the golden ratio which arises from a simple 
 question about rectangles and proportion. A slightly different natural ques
 tion 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 an
 d 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 fi
 nal construction involving copies of the Fibonacci sequence itself.</p>
CONTACT:David Nacin, William Patterson University
X-EXTRAINFO:https://rutgers.zoom.us/j/94346444480\nPassword:6564120420
DTSTAMP:20260827T043221
DTSTART;TZID=America/New_York:20210304T170000
DTEND;TZID=America/New_York:20210304T180000
SEQUENCE:0
TRANSP:OPAQUE
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