Table of Contents
What numbers are both triangular and square?
From (1), we get S(3) = 41616, whereas there is another number, 1225, that is both triangular and square: 1225 = 49·50/2 = 352.
Can a number be triangular and square?
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a perfect square.
Which 2 digit number is a square number as well as triangular number?
25,36,4964 Ans. (4) Write the greatest two digit square numbers as well as triangular numbers.
What is the smallest number that is both triangular and square?
That it is both a triangular number AND a square number is pretty remarkable. But guess what? 1225 is ALSO a hexagonal number. In fact, 1225 is the smallest number greater than 1 that is a triangle, a square, AND a hexagon!
Is 2015 a triangular number?
This is the Triangular Number Sequence: 1, 3, 6, 10, 15, 21, 28, 36, 45.
Is 41616 a triangular number?
(OEIS A001108 and A001109), corresponding to the triangular square numbers 1, 36, 1225, 41616, 1413721, 48024900. (OEIS A001110; Pietenpol 1962). In 1730, Euler showed that there are an infinite number of such solutions (Dickson 2005).
Is there a perfect square of 1225?
The square root is the number (integer) which when multiplied by itself results in the original number. The 2nd root of 1225 is +35 or -35. This shows that 1225 is a perfect square.
What are the numbers that are both Square and triangular?
Square Triangular Numbers. The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, and so on, given by the formula n(n+1)/2. Notice that the numbers 1 and 36 on this list are perfect squares as well as triangular. A standard problem in elementary number theory is to determine ALL the numbers that are both square and triangular.
What is the difference between two consecutive triangular numbers?
The difference between the squares of those two consecutive triangular numbers is equal to a cube. The sum of those four cubes is equal to the square of the fourth triangle. Alternatively, since every square number is the sum of consecutive odd numbers, so is the square of a triangular number.
How do you find the kth square of a triangle?
Therefore for any given k we can find the kth square triangular number. The a value will give us the square number required and the b value will give us the triangular number required. For example with k = 3: This tells us the 3rd square triangular number is the 35th square number or the 49th triangular number.
Is 36 a square or triangular number?
Square Triangular Numbers Square triangular numbers are numbers which are both square numbers and also triangular numbers – i.e they can be arranged in a square or a triangle. The picture above (source: wikipedia) shows that 36 is both a square number and also a triangular number.