## 2019 - 22nd Annual Steven Galovich Memorial Student Symposium

#### Presentation Title

Playing with Triangular Numbers

Mathematics

Lillard 132

#### Abstract

A triangular number is a number N that satisfies that N dots can be arranged in increasing order to form an equilateral triangle. A triangular number N can be represented in the form N = n(n+1)2 , for some positive integer n.

In the article “Playing With Blocks”, McMullen noticed that sometimes, there are consecutive sequences of triangular numbers that add up to form another triangular number. For example 1 + 3 + 6 = 10, where k is the number of triangular numbers added. He asked the following question: “Every value of k except k = 4 that I looked at yields at least one valid solution. Is there a k > 4 where our problem has no solution?” So in our work we proved the following theorem, derived from McMullen’s question:

Theorem: Let k > 4 be a square. Then there exist k consecutive triangular numbers that add up to a triangular number.

#### Presentation Type

Individual Presentation

#### Start Date

4-9-2019 10:30 AM

#### End Date

4-9-2019 11:45 AM

#### Panel

Research that Counts: Applied Insights and Theoretical Provocations

#### Panel Moderator

DeJuran Richardson

Mathematics

#### Share

COinS

Apr 9th, 10:30 AM Apr 9th, 11:45 AM

Playing with Triangular Numbers

Lillard 132

A triangular number is a number N that satisfies that N dots can be arranged in increasing order to form an equilateral triangle. A triangular number N can be represented in the form N = n(n+1)2 , for some positive integer n.

In the article “Playing With Blocks”, McMullen noticed that sometimes, there are consecutive sequences of triangular numbers that add up to form another triangular number. For example 1 + 3 + 6 = 10, where k is the number of triangular numbers added. He asked the following question: “Every value of k except k = 4 that I looked at yields at least one valid solution. Is there a k > 4 where our problem has no solution?” So in our work we proved the following theorem, derived from McMullen’s question:

Theorem: Let k > 4 be a square. Then there exist k consecutive triangular numbers that add up to a triangular number.