1. TRIANGLE NUMBERS

2. Consecutive triangle numbers add up to a square number
INTERESTING FACT 1
Consecutive triangle numbers add up to a square number

3. 8 x Triangle number +1= square number (odd)
INTERESTING FACT 2
8 x Triangle number +1= square number (odd)

4. Tk-1 Tk ka Ta

5. Tk-1 Tk ak Ta

6. Then the odd squares are (2a + 1)2 and (2b + 1)2
The sum of two odd squares
Subtract 2, then divide by 8
Ta + Tb
Then the odd squares are (2a + 1)2 and (2b + 1)2  

7. Fascinating Triangle Numbers by Shyam Sunder Gupta

14. Consecutive triangle numbers add up to a square number
INTERESTING FACT 1
Consecutive triangle numbers add up to a square number