Is 523 a triangular number? (Is 523 a triangle?)

Is 523 a triangular number?

Here we will define and determine if 523 is a triangular number, also known as a triangle number. First, note that an equilateral triangle is a triangle where the length of the three sides are the same, and the three internal angles of the triangle are 60 degrees. An equilateral triangle can look like this:

Take notice of the symmetry of the dots inside the triangle above. Each side of the triangle has the same number of dots, and one dot is added to each row of dots.

523 is a triangular number if we can arrange all 523 dots or objects in perfect symmetry to make an equilateral triangle. To determine if a number (n) is a triangular number, the following equation must be true:

√(8 × n) +1 = Integer

When we enter 523 for n in our formula, we get the following result:

√(8 × 523) +1 ≈ 64.6916

64.6916 is not an integer (whole number), therefore the answer to "Is 523 a triangular number?" is as follows:

523 = Not a triangular number

Since 523 is not a triangular number, you cannot use 523 objects or dots to create a symetric equilateral triangle similar to the one pictured above on this page.

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