Exploring Brackets in Risp and Factorisation Patterns
Discover the interesting concept of brackets in Risp, explore permutations of non-zero integers, and delve into factorisation patterns. Compare notes with colleagues, make conjectures, and notice intriguing recurring factors. Does the starting list of numbers matter? Dive into these questions and more in this thought-provoking content.
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Presentation Transcript
Brackets out, brackets in Risp 3
BRACKETS OUT, BRACKETS IN Pick three different, non-zero integers between -5 and 5 that don t sum to zero. Place all of the permutations of these numbers in the boxes below.
BRACKETS OUT, BRACKETS IN Multiply them all out. Then add all the results together. Now take this sum: can you factorise it? Compare notes with your colleagues once you have tried to do this. Do you notice anything? Does it matter what the starting list of numbers is? Can you make any conjectures? Can you prove these?
BRACKETS OUT, BRACKETS IN ? ? ? ??2 + (?? + ?)? + ?? ? ? ? ??2 + (?? + ?)? + ?? ? ? ? ??2 + (?? + ?)? + ?? ? ? ? ??2 + (?? + ?)? + ?? ? ? ? ??2 + (?? + ?)? + ?? ? ? ? ??2 + (?? + ?)? + ?? ?(? + ? + ?) ?? + ?(?? + ?? + ?? + ? + ? + ?)? + ?(?? + ?? + ??)
BRACKETS OUT, BRACKETS IN ? ? + ? + ? ?? + ? ?? + ?? + ?? + ? + ? + ? ? + ? ?? + ?? + ?? ? ? + ? + ? ??+ ?? + ?? + ?? + ? + ? + ? ? + ?? + ?? + ?? ? ? + ? + ? ??+ ?? + ?? + ?? ? + ? + ? + ? ? + ?? + ?? + ?? ? ? + ? + ? ??+ ? + ?? + ?? + ?? ? + ? ? ? + ? + ? ? ? + ? + ?? + ?? + ?? ? + ? ? ? + ? + ? ? + ?? + ?? + ?? ? + ? So ? + ?is always a factor.
BRACKETS OUT, BRACKETS IN Pick three different, non-zero integers between -5 and 5 that don t sum to zero. Place all of the permutations of these numbers in the boxes below. SIC_9
BRACKETS OUT, BRACKETS IN Pick three different, non-zero integers between -5 and 5 that don t sum to zero. Place all of the permutations of these numbers in the boxes below. SIC_9
