Science & education writer · View profile
· 6 min read
The upward force equals the weight of the fluid pushed aside. That one sentence decides whether something floats, and if it floats, exactly how much of it stays under.
· 7 min read
Five variables, four equations, and each equation is missing exactly one of them. Choose by looking at the variable the question never mentions.
· 6 min read
Three formulas cover the whole of projectile motion on level ground. The catch is level ground: the moment launch and landing heights differ, the 45° result stops being true.
· 7 min read
PV = nRT holds when the gas is dilute and far from condensing. The value of R depends entirely on the units you feed it, and the temperature is never in degrees Celsius.
· 3 min read
Split a bill and tip evenly across a group. Learn the tip percentage, total, and per-person formulas with a clear worked example so nobody over- or underpays.
· 4 min read
Life expectancy is an actuarial average by age and sex, not a personal prediction. Learn how life tables work, why the figure rises as you age, and how to read the numbers.
· 4 min read
Estimate your retirement age from how many years it takes your savings to reach a target. Learn the growth formula, a worked example, and why the target matters most.
· 9 min read
Solve for the missing term, then convert the answer into a bench instruction. The step almost everyone skips is that the solvent you add is V2 minus V1, not V2.
· 8 min read
One half-life leaves 50%, three leave 12.5%, ten leave less than a tenth of a percent. The formula is a single line — the part worth understanding is why the answer never reaches zero.
· 4 min read
Estimate reading time from word count and reading speed. Learn the simple formula, the average of about 250 words per minute, and a worked example for a full novel.
· 7 min read
The phase cycle takes 29.53 days but the orbit takes only 27.32, and the 2.21-day gap is the entire explanation. With the eight phases, their illumination, when each rises and sets, and how they flip south of the equator.
· 7 min read
Every problem in the chapter is the same four moves. The mole ratio is the hinge, and it is the step students lose — worked here end to end, limiting reactant and percent yield included.
· 7 min read
Four routes for four kinds of solution, each worked with real numbers. Including the part most pages leave out: the square-root formula for a weak acid is an approximation with a validity limit, and it fails quietly.
· 6 min read
Multiply each atomic weight by its subscript and add. The only three places the arithmetic goes wrong are a subscript after a closing bracket, the hydrate dot, and a capital letter typed as a lowercase one.
· 14 min read
A four-year public in-state budget is 30,990 dollars today. Eighteen years out at 4 percent cost inflation the same four years cost 266,593 — 2.15 times the sticker you can see now. And the sticker was never the price: the average net cost of attendance is 21,340.
· 4 min read
A fair draw needs more than a random number: equal probability, no reuse of a biased method, and a result someone else can check. Here is how to run one.
· 4 min read
The Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.
· 17 min read
We measured the coverage curve of French on 313 million words of subtitles: the top 1,000 forms account for 80.77% of running text. Then we took a normal French sentence in which 80% of the tokens are inside that top 1,000, and showed that a reader who knows every one of them learns nothing from it.
· 4 min read
A z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.
· 3 min read
Convert between degrees and radians with radians = degrees × π/180 (and back with × 180/π), understand why 180° = π, and learn the common angles by heart.
· 5 min read
A grade average is the weighted mean of your grades: each grade times its weight, summed, divided by the total weight. Learn the method, a worked example, and how GPA differs from a percentage.
· 4 min read
Use the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.
· 4 min read
Daylight saving time shifts clocks an hour in spring and back in autumn. Learn spring-forward and fall-back, why one day is 23 hours and another 25, and how US and EU dates differ.
· 4 min read
Find the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.