Blog
How graphing calculators work, where they go wrong, and the mathematics behind the pictures.
- · 8 min read
Why graphing calculators draw fake vertical lines at asymptotes
The vertical lines at the asymptotes of tan x and 1/x aren’t part of the graph. Why they appear, why more samples don’t help, and what does.
- · 10 min read
Interval arithmetic: how a plotter can prove where a curve is
Sampling plotters can miss curves that touch zero without crossing it. Interval arithmetic computes with ranges, so a plotter can prove where a curve is.
- · 9 min read
Why sin(π) isn’t zero on a computer, and how to fix it
Computers say sin(π) = 1.22 × 10⁻¹⁶ and 0.1 + 0.2 = 0.30000000000000004. Why floating point does this, and how a calculator gives the expected answer.
- · 9 min read
How to draw a slope field, by hand and online
How to draw a slope field by hand, step by step: compute the slopes, sketch solution curves, find equilibria, and match equations to slope fields.
- · 9 min read
What R² doesn’t tell you: reading a regression properly
Four data sets with the same regression line and the same R², and completely different stories. How to read residuals, standard errors and bands.
- · 8 min read
Domain colouring: how to see a complex function
A complex function needs four dimensions to graph. Domain colouring fits it in a picture: hue for the angle, brightness for the size. Reading zeros and poles.
- · 10 min read
The best free graphing calculators in 2026, compared honestly
Desmos, GeoGebra, NumWorks, Wolfram|Alpha and ihateDesmos compared: what each free graphing calculator does best, and which to use when.
- · 9 min read
18 graphing calculator tricks that save time
Restrict domains, draw families with lists, graph derivatives, find intersections, fit data and use units: 18 practical graphing calculator tips.
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