You may also like

problem icon

Forgotten Number

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

problem icon

Man Food

Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?

problem icon

Sam Again

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

Triangle numbers 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 rectangle?

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 numbers.

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, 2092035

Deduce a strategy for working out any triangle number.


Extension:

Consider the following numbers: $4851, 6214, 3655, 7626, 8656$.

Which are triangle numbers?
How did you decide?

Do any triangle numbers end $000$?

 

 

You may wish to try the problems 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 numbers.




The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2016. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.