Investigation Gallery

Here at NRICH we believe that mathematical explorations and investigations can really help young mathematicians to develop their skills, knowledge and interest in and of mathematics. One of the wonderful things about mathematics is that it offers the chance for discovery of ideas and structure beyond the things about which you have learned or been taught. 

Here we are hoping to host some of the investigations, explorations and articles done by young mathematicians around the world. If you are proud of a piece of your work why not write it up carefully and send it to us? See the foot of this page for details of how to go about this. We will link each hosted investigation to Ask NRICH, so should one of our readers wish to comment they will be given the opportunity to do so.

Happy investigating!

Rangan's Theory of Cycles

Age 14 to 18

In this beautifully written-up investigation Abhay describes his discovery of a 'theory of cycles'.


To send us a piece of mathematics you will need to write it up carefully and email it to us in pdf form (to For us to host the work the following will need to hold:
  • It needs to be pitched at the level of a typical keen upper secondary student (14-19).
  • It needs to be of general mathematical interest
  • It needs to be presented to a high standard
  • It needs to be mathematically essentially correct (We won't edit or correct any submissions, so please take care with the submission)
If we think that it would be in the right sort of style and level then we will host it as in the other examples. It can be on any aspect of mathematics and it might be something that you have discovered, extended, visualised, presented or solved in an interesting way. Please include the way in which you would like to be attributed along with gender for the use of his/her in the text (sometimes we are unfamiliar with names from various countries). Please also include a contact email address so that we can let you know if and when your work will appear on the site.

Note that:
  • You will need to be happy for us to link the resource to Ask NRICH.
  • The NRICH team themselves will not be able to engage in discussion with you about your work.
  • We will periodically take a look at all of the submitted material during the university vacations, so please be prepared for a reasonably long delay.
  • If we don't think that your work is suitable for inclusion here please don't be disheartened!
  • We reserve the right to remove or edit material at any time.