The S r 3  formula

Draw a 1 cm square

Now draw a 2 cm square to touch the first at a corner only

Finally draw a ‘border’ that produces a 3 cm square :  

Write in the dimensions of each sector of your diagram

This seems to indicate that :  

3 ² = ( 1 + 2 )² =  1² +  2² + 2 lots of ( ½.2² )

                           =  1.1² + 2. 2²

                           =   13   +  23

 i.e.                   13   +  23 = ( 1 + 2 )²

Draw some larger versions of this diagram, and see whether you have a general result. 

Use your formula to predict the value of 13 + 23 + 43 + 53 ... + 103

Check it with a calculator !

Open the File as a Word Document

 

Send site mail to admin@1000problems.org  or personal comments direct to sdakeyne@psc.ac.uk with questions or comments about this web site.
Last modified: June 18, 2007