STEM Explainer

Sample snippets

Short snippets from across the STEM subjects. Anything formula-, equation- or law-shaped is highlighted — tap it to open a plain-language explanation in the Tutor panel. Ordinary prose, even when it describes a process, stays untouched.

Force and motion

On the linear-track rig, each run loaded the sled with a different mass while a sensor logged how quickly it sped up. Writing up the lab, the group reached for F = ma to check whether their measured accelerations lined up with what the theory predicted.

Reactions and compounds

The fuel-cell demo drew hydrogen from a small cylinder and passed it over the oxygen electrode while the class watched droplets gather at the outlet. The change written on the board, 2H₂ + O₂ → 2H₂O, was the same one powering the bus parked outside.

Later that week the group looked at what plants build for themselves. Green plants feed through photosynthesis, taking in light, carbon dioxide and water and giving off oxygen as they lay down energy stores. When a leaf sample was run through the analyser, the sugar it had stored showed up on the trace as C₆H₁₂O₆.

Curve sketching

Halfway through the problem set the class swapped their calculators for graph paper. The next question asked them to sketch y = x² − 5x + 6 and mark clearly where the curve met each axis.

Polar curves

Not every equation is easiest to picture from the text alone. This one traces a figure-eight in polar coordinates — tap the graph to explore it step by step.

r² = 36 cos(2θ)

Tap to explore the graph →

Population growth

Twelve seasons of counts showed the island's deer herd rising fast at first, then flattening out as the winters grew harder. To capture that slowdown, the field team fitted their data to dN/dt = rN(1 − N/K) and let the model do the rest.

Electrical circuits

Before powering up the test rig, the technician noted the supply voltage and measured the coil's resistance. A quick pass through V = IR told her whether the fuse she'd fitted could take the current.

Conditional probability

The screening trial kept flagging healthy volunteers, which unsettled the team more than the occasional miss did. Before the next round they sat down and reworked the numbers from scratch, starting from the rule itself:

P(A|B) = P(B|A) P(A)P(B)

Algorithm complexity

The pull request swapped out the old sort, and in review the lead circled one line of the summary: the hot path was now O(n log n). That was the difference between the nightly job finishing before morning and not.