A staircase
Slope
Some staircases feel easy, others leave you breathless. The difference isn't the height. So what is it?
Three ways to see it
Eight steps, one floor up. Every step is identical to the last: same height, same depth. That repetition isn't an accident — it's exactly what makes a staircase safe to climb.
Switch layers — the scene stays put
What's really going on
Slope isn't a number, it's a ratio — and being a ratio changes everything. Measure it at the first step or the last, across two steps or six, and you get the same answer: 0.58. That never-changing ratio is the definition of a straight line. A curve is something whose slope changes from point to point; a line is something whose slope doesn't. It's also why building rules limit stair ratios — after one step your foot learns where the next one lands and never has to think again.
The equation
m = Δy / Δx
Δ (delta) means 'change'. Divide the vertical change between two points by the horizontal change. If the answer is the same everywhere, what you have is a straight line.
Same concept, elsewhere
Memorising one example gets you nowhere. You need to spot the concept wherever it turns up.
A wheelchair ramp — building rules cap the slope at 1/12; that number isn't paperwork, it's the ratio a wheel can actually climb
A road sign reading '8% slope': you drop 8 metres for every 100 you travel
How steep a roof is — the smallest ratio that makes rain run off instead of collecting on top
The rate of a price rise on a chart: vertical change ÷ elapsed time
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