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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Excel Investigation: Pythagorean Triples
Stage: 3 and 4
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Find sets of three numbers so that the sum of the squares of the first two is equal to the square of the third, as in (3, 4, 5) or (5, 12, 13).
for problems with two independent variables create a table of all possible first and second number combinations to see which of these provide integer results for the square root of the sum of their squares.
The formula for the first cell is =SQRT(B$1^2+$A2^2) which is then copied across the chosen range. Then look for cells in which this formula returns integer values. Conditional formatting helps identify the values of interest. The colour change occurs when a cell value is exactly equal to its integer part. The red type on a tan background are genuine integers, and are the result of the conditional formatting being activated. The other integers in the sheet are caused by Excel rounding the display value to 2 digits even though the held value may have many decimal places, as increasing the width of a column would reveal.
Look at the 10% Zoom View and account for the patterns you observe.
Meet the team
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.
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Millennium Mathematics Project