Below you will find a little theorem about square numbers and triangle numbers. Instead of a proof, I included a large number of hints; so feel encouraged to play with the terms, to find out their properties and to prove your own conjectures.
When you have no idea which step to make next, or if you want to compare your solutions with mine, simply click on the statement in question to get a hint. Some statements may also hide multiple hints; you can get them one after another by clicking repeatedly on the original statement. When you click on some hint, you will often get a more detailed hint for it, if there is one. Simply start by clicking on the definition to get the first problem; then click more carefully, if you want to develop your own ideas without having been influenced too much by my thoughts.
In order to limit the number of WEB pages to be prepared, I decided to close automatically all hints not lying directly on the path to the last requested hint, but I hope to circumvent this restriction in a future version.
At this point, I want to express my thanks to my colleague Tobias Wirnsberger, who formulated and proved a first a similar theorem, and thereby inspired me to prepare this presentation in the WEB.
View the theorem in hypertext form
Download the theorem in hypertext form
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