Loci

## Middle and High School

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Now we briefly look at what middle and high school students and their teachers can get out of Wolfram|Alpha.

Wolfram|Alpha easily handles routine algebra problems such as finding the equation of a line through two given points, factoring polynomials, or solving quadratic equations. With Mathematica as its engine, it naturally can also solve cubic and quartic equations or arbitrary systems of linear equations.

But if you enter the query "graph y=3x+5" you get two graphs. The first appears to have a negative y-intercept and a positive x-intercept. The confusion arises because we expect the axes to intersect at the origin, but Wolfram|Alpha puts scales on horizontal and vertical lines that do not represent the coordinate axes. The query "graph y=3x+5 from x=-1 to x=1" gives a different graph with a break in the y-axis to show that a piece of the y-axis has been excised. It is not clear how to force Wolfram|Alpha to put the "AxesOrigin" at (0,0).

Wolfram|Alpha can list and depict the regular platonic solids, but does not know what to do with the query "Prove that the base angles of an isosceles triangle are congruent." It can evaluate cos(36 degrees) exactly, but is stumped by "If two angles of a triangle are 36 degrees and 72 degrees, what is the third angle?"

Once again we can easily see the power and the limitations of this new technology.

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[Note: Contents of frame come from wolframalpha.com and are not maintained by Loci]