- A
triangular number or
triangle number counts objects arranged in an
equilateral triangle.
Triangular numbers are a type of
figurate number,
other examples...
-
triangular number and a
square number.
There are
infinitely many
square triangular numbers; the
first few are: 0, 1, 36, 1225, 41616, 1413721, 48024900, 1631432881...
- tetrahedron. The nth
tetrahedral number, Ten, is the sum of the
first n
triangular numbers, that is, Ten=∑k=1nTk=∑k=1nk(k+1)2=∑k=1n(∑i=1ki){\displaystyle Te_{n}=\sum...
-
different sets of
numbers,
generalizing from
triangular numbers to
different shapes (polygonal
numbers) and
different dimensions (polyhedral
numbers). The term...
- one type of 2-dimensional
figurate numbers. The
number 10 for example, can be
arranged as a
triangle (see
triangular number): But 10
cannot be arranged...
- 4095 is the
largest of five Ramanujan–Nagell
numbers that are both
triangular numbers and
Mersenne numbers of the
general form. The sums of the
first five...
-
triangular number. In the
sequence of
triangular numbers,
indexed powers of 10 in this
sequence generate the
following sequence of
triangular numbers...
-
square numbers are a type of
figurate numbers (other
examples being cube
numbers and
triangular numbers). In the real
number system,
square numbers are non-negative...
- used to
approximate the
square root of two, Pell
numbers can be used to find
square triangular numbers, to
construct integer approximations to the right...
-
perfect numbers are not
trapezoidal numbers; that is, they
cannot be
represented as the
difference of two
positive non-consecutive
triangular numbers. There...