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In this problem we are going to consider triangle numbers.
Your aim is to find a method for working out the value of any
You will then be able to use your method to identify quickly
whether numbers are triangular.
can be represented by a triangular array of squares.
Imagine two copies of a triangular array of
squares. Can you picture how to fit them together to make a
rectangle? What is special about the dimensions of your
Use the activity below to test your ideas.
This text is usually replaced by the Flash movie.
What do you notice about doubling triangle numbers?
Experiment with different triangle numbers and explain what is
special about the rectangles made from two identical triangle
Can you write down the dimensions of the rectangle made from two
copies of the 250th triangle number? Can you use this to work out
the 250th triangle number?
Check - your answer should be
somewhere in this list: $29184, 31375, 586594, 908475,
Have you a strategy for finding any triangle number?
If your strategy works, write down your method as clearly as you
Consider the following numbers: $4851, 6214, 3655, 7626, 8656$.
Which are triangle numbers?
Describe a quick way of deciding.
Do any triangle numbers end $000$?
You may wish to try the
Mystic Rose and
Handshakes. Can you see why
we chose to publish these three problems together?
You may also be interested in
reading the article Clever Carl, the story of a young mathematician
who came up with an efficient method for adding lots of consecutive