Tähtarvuline

Tähtarvuline is an Estonian term that translates to "star number" or "stellar number." It refers to a specific type of figurate number, which are numbers represented by a geometric arrangement of dots. In the case of tähtarvuline, the arrangement forms a star.

The nth tähtarvuline is calculated using the formula n(2n - 1). For example, the first tähtarvuline (n=1) is 1(2*1 - 1) = 1. The second (n=2) is 2(2*2 - 1) = 2 * 3 = 6. The third (n=3) is 3(2*3 - 1) = 3 * 5 = 15. The sequence of tähtarvuline begins with 1, 6, 15, 28, 45, and so on.

Geometrically, tähtarvuline can be visualized by arranging dots in concentric star shapes. The first star consists of a single dot. The second star is formed by adding six dots around the central dot, creating a six-pointed star shape. Each subsequent star is formed by adding more dots in a way that maintains the star pattern.

Tähtarvuline are a subset of polygonal numbers and have connections to other number sequences. They are sometimes explored in recreational mathematics and number theory due to their interesting properties and patterns. The concept of figurate numbers, including tähtarvuline, has a long history, dating back to ancient Greek mathematicians.