







Triangular numbers that are square 
20111227 

From Luke: The “TnS” is a positive integer which is both Triangular number
and Square number. For example, 36 is a “TnS” number
since 36=1+2+3+4+5+6+7+8 (Triangular number)
and 36=6x6 (Square number).
What is the next “TnS” which is greater than 36? Answered by Penny Nom. 





A champagne pyramid 
20100322 

From Kathy: I have 680 champagne glasses and my pyramid can only be 15 levels high. How many glasses need to be on each level? Is there a formula I can use? Answered by Robert Dawson. 





Triangular Numbers 
20090616 

From Chinonyerem: Question from Chinonyerem, a student:
Each of the numbers
1 = 1, 3 = 1+2, 6 = 1+2+3, 10 = 1+2+3+4 ,...
represents the number of dots that can be arranged evenly in an equilateral
triangle:
.
. . .
. . . . . ...
. . . . . . . . . .
This led the ancient Greeks to call a number TRIANGULAR if it is the
sum of consecutive integers, beginning with 1. Prove the following facts
concerning triangular numbers:
(a) A number is triangular if and only if it is of the form n(n+1)/2 for some n >= 1
(b) The integer n is a triangular number if and only if 8n+1 is a perfect square
(c) The sum of any two consecutive triangular numbers is a perfect square
(d) If n is a triangular number, then so are 9n+1, 25n+3, and 49n+6 Answered by Penny Nom. 





The number of blocks on the face of a pyramid 
20070627 

From Heather: I was wondering if there was an equation in order to calculate the number of blocks on the face of a pyramid.
For example:
X
X X
X X X
Is there a specific formula in order to calculate that there are
6 blocks here?
Thank You,
Heather Answered by Harley Weston. 





1, 3, 6, 10... 
20061215 

From Lisa: What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser. Answered by Stephen La Rocque and Penny Nom. 





A triangle of 50p pieces 
20060222 

From Stuart:
Ok, so i am collecting 50p pieces and arranging them on my desk in the shape of a triangle.
eg
50p
50p 50p
50p 50p 50p
50p 50p 50p 50p
I want to work out how much money I'm saving just by knowing how many rows of coins there are. If i can work out how many coins there are just by knowing how many rows I have I can just divide by 2 to find out the amount in dollars.
Answered by Penny Nom. 





Triangular numbers 
20020426 

From Anika: Can you please tell me what a triangular number is? Answered by Penny Nom. 





Triangular numbers and square numbers 
20000302 

From Emily McCallum: Would someone find me some math activities using triangular numbers and square number. Especially acitivities that actually form the shapes. They need to be at the 5th grade or 6th grade level. But you can not find anything that can be tauht at these level, that fine. I just need to be able to teach this new subject or kind of math to my kids. Answered by Rick Seaman and Penny Nom. 





Cannonballs 
19990127 

From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom. 





Triangular Numbers 
19981030 

From Matt: i would like to know about triangular numbers and it history i would also like to know about the history of prime numbers thank you Answered by Chris Fisher. 





Triangular Numbers. 
19970908 

From Rachel: Show visually that the square number 16 is the sum of two triangular numbers. Which two? Answered by Penny Nom. 

