MATC Mathematics Club
Lecture #85
Madison Area Technical College
Madison, Wisconsin
Professor Norbert J. Kuenzi Ph.D., UW- Oshkosh
"What are Trapezoidal Numbers?"
Previous Lectures: (#74 "The Tower of Hanoi Puzzle"), (#7"Some Binary Curiosities") , (#43"How many Coconuts?--The Famous Monkey, Sailors, and Coconuts Problem") , (#63"Some (Sum) Numerical Curiosities for 2007"), (#16 "Two men thinking about math recreations")
Abstract: Students have often been introduced to square numbers, cubic numbers, and triangular numbers. The names square, cubic, and triangular are given because the so named numbers can be displayed as an array of dots with the geometric shape named.
Numbers which can be written as a sum of two or more consecutive whole numbers can be displayed as a trapezoidal arrangement of dots and hence are called trapezoidal numbers. We will explore these numbers and try to answer some questions. Is 2009 a trapezoidal number? Which whole numbers are not trapezoidal numbers? Which whole numbers can be represented as trapezoidal numbers in two ways? Three ways? Four ways? Four Hundred ways?
Biography: Norbert J. Kuenzi Professor Ph.D. (1969); University of Iowa Research Interest: Probability
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