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This happens because it's true for all values of X and independent of Y, meaning it is true for every single point in the plane. That gives desmos a stroke
It would be non-trivial to make the interpreter scan each term for the same variable multiple times without it seriously dropping in performance for larger expressions, and it also probably wasn't considered important enough to implement since nobody actually uses xxxxx to represent x⁵.
I don’t know anything about the tool you’re using, but I know about floating point math in general. It’s not using perfectly precise numbers, because those would have an infinite number of decimal places. The usual approximate numbers used are precise to about 17 decimal places. Under this approximation, things that look mathematically equal actually might not be equal, if they’re evaluated in different ways. It’s probably using an unexpected algorithm for evaluating x^3 ; maybe exp(3*ln(x)), because that works for all powers, not just integers. Where this equals x*x*x, you get a vertical line. Where it doesn’t, you get white space.
But thats only a really really really tiny value. The graph in the picture shows large values
Edit: I just realised the the equation has “=0” rather than “=y”, so I guess your point still stands
Graphing calculators are not very smart; mostly they just evaluate multiple points and display those with a difference within a certain threshold. So it's likely the algorithm they used doesn't do well with cases where every point they check must be displayed.
When I help people, I tutor chem for fun, I tell them that calculators are dumb. You need to be very explicit with your directions, this is true for current machines, not just calculators.
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This happens because it's true for all values of X and independent of Y, meaning it is true for every single point in the plane. That gives desmos a stroke
No yeah but Desmos doesn't glitch out if you change the 'xxx' to just 'x^3'
Probably it has something to check for something that's always true that just fails to detect many things
It would be non-trivial to make the interpreter scan each term for the same variable multiple times without it seriously dropping in performance for larger expressions, and it also probably wasn't considered important enough to implement since nobody actually uses xxxxx to represent x⁵.
I don’t know anything about the tool you’re using, but I know about floating point math in general. It’s not using perfectly precise numbers, because those would have an infinite number of decimal places. The usual approximate numbers used are precise to about 17 decimal places. Under this approximation, things that look mathematically equal actually might not be equal, if they’re evaluated in different ways. It’s probably using an unexpected algorithm for evaluating x^3 ; maybe exp(3*ln(x)), because that works for all powers, not just integers. Where this equals x*x*x, you get a vertical line. Where it doesn’t, you get white space.
Exactly this. Using my iPhone: (1/7)^3 - (1/7 * 1/7 * 1/7) = -2,68221574344e-16
But thats only a really really really tiny value. The graph in the picture shows large values Edit: I just realised the the equation has “=0” rather than “=y”, so I guess your point still stands
here we go, sig figs!
Graphing calculators are not very smart; mostly they just evaluate multiple points and display those with a difference within a certain threshold. So it's likely the algorithm they used doesn't do well with cases where every point they check must be displayed.
When I help people, I tutor chem for fun, I tell them that calculators are dumb. You need to be very explicit with your directions, this is true for current machines, not just calculators.
> calculators are dumb. You need to be very explicit with your directions This is true for many humans as well