Triangular numbers represent the number of points within an equilateral triangle that is filled uniformly with points. The formula for a triangular number "n" is equal to the number of points in a triangle with "n" points on each side. Triangular numbers have links to other figurate numbers, such as the sum of two consecutive triangular numbers equalling a perfect square, which is the difference between the numbers.

1. Triangular numbersTriangular numbers
●●Mihailescu ArinaMihailescu Arina
●●Calin PetreCalin Petre
●●Pavel IsabellaPavel Isabella
●●Constantin MariaConstantin Maria

2. What is a triangular number?What is a triangular number?
 A triangular number is theA triangular number is the
number of points within annumber of points within an
equilateral triangle that isequilateral triangle that is
filled uniformly withfilled uniformly with
points/dots.points/dots.
-example:-example:
-Three is a-Three is a
triangular number becausetriangular number because
the triangle is made out ofthe triangle is made out of
three non-collinearthree non-collinear
points/dots.points/dots.

3. The formula for the triangularThe formula for the triangular
numbernumber
 The triangular number “The triangular number “nn” is equal to the” is equal to the
number of points/dots of the triangle innumber of points/dots of the triangle in
which the side has “which the side has “nn” points/dots.” points/dots.
-example:-example:
TT66=1+2+…+(6-1)+6=6*(6+1):2=[6^(2)+6]:2=1+2+…+(6-1)+6=6*(6+1):2=[6^(2)+6]:2

4.  Triangular numbers have a wideTriangular numbers have a wide
variety of links with figuratevariety of links with figurate
numbers. The easiest one is that thenumbers. The easiest one is that the
sum of two consecutive triangularsum of two consecutive triangular
numbers is a perfect square, morenumbers is a perfect square, more
exactly the difference between theexactly the difference between the
numbers.numbers.

5.  This can also be demonstratedThis can also be demonstrated
graphically :graphically :
6+10=16 10+15=256+10=16 10+15=25

6. SOURCESSOURCES
http://ro.wikipedia.org/wiki/Num%C4%83r_triunghiularhttp://ro.wikipedia.org/wiki/Num%C4%83r_triunghiular

7. THANK YOU!THANK YOU!