Q:
# What Is the Relationship Between Square and Triangular Numbers?

A triangular number is one that is the sum of all positive integers less than or equal to a given positive integer. A square number is the product of an integer multiplied by itself. A square triangle is both a square and a triangular number. There is no specific relationship between square and triangular numbers, other than the fact that some triangular numbers are also square.

Continue ReadingAn example of a square triangle is 36, because 36 is the sum of all positive integers less than or equal to 8, making it a triangular number, and is also the product of 6 x 6, making it a square number. It is important not to confuse a triangular number with a cube. A cube is the product of an integer multiplied by itself three times. For instance, 27 is a the product of 3 x 3 x 3. Since triangles have three sides and cubes are multiplied three times, beginner math students sometimes confuse these concepts.

It is possible to find the equation giving all numbers that are both square and triangular by setting the equation of a square number (m^2) equal to the equation of a triangular number (n(n+1)/2) and then solving for n. This leads to the equation n = (-1 + sqrt(1 + 8m^2))/2. It should be noted that this result is only valid if n is a positive integer; thus the equation is restricted by the condition that 1 + 8m^2, the value under the root, must be a square number.

Learn more about Numbers-
Q:
## What Are Rational and Irrational Numbers?

A: Rational numbers are numbers that can be expressed as the ratio of two integers, whereas irrational numbers cannot be expressed as a ratio of integers. Irr... Full Answer >Filed Under: -
Q:
## Are All Integers Rational Numbers?

A: All integers are rational numbers. A rational number is in the form a/b, where "a" and "b" are integers, and "b" is not equal to zero. Integers are a subse... Full Answer >Filed Under: -
Q:
## How Do You Place Rational Numbers in Order From Least to Greatest on a Number Line?

A: Rational numbers are any numbers that can be expressed by a fraction with integers in both the numerator and the denominator. The amount of time and paper ... Full Answer >Filed Under: -
Q:
## What Are Some Facts About the Number 55?

A: The number 55 is the largest Fibonacci number to be both triangular and semi-prime. Also, any odd number between 90 and 110 multiplied by 55 would result i... Full Answer >Filed Under: