Day 2 — Percentages
Time: ~20 min · Topic: percentages
The problem
A pair of sneakers costs $80, but they're on sale for 25% off. How much do you save?
Hint: Think about what "25 percent" really means — it's 25 out of every 100. So for every $100, you'd save $25. But these shoes cost less than $100…
Try it yourself
Take a few minutes. Don't peek at the steps. If you get stuck, the hint above is enough to nudge you forward.
Step-by-step solution
- Convert 25% to a decimal → 25% = 25/100 = 0.25
- Multiply the original price by 0.25 → $80 × 0.25 = $20
- You save $20 on the sneakers!
Answer: You save $20. The sneakers now cost $80 − $20 = $60.
Why this matters
The word "percent" comes from the Latin "per centum," meaning "by the hundred" — and ancient Romans actually used fractions based on 100 to calculate taxes over 2,000 years ago!
This day in math: The Mathematician Who Won Olympic Silver
April 22, 1887 · Harald Bohr
On this day in 1887, Harald Bohr was born in Copenhagen, Denmark. Before becoming one of the 20th century's most original mathematicians, Bohr was a star footballer who won a silver medal at the 1908 London Olympics. Playing for Denmark, he helped crush France 17-1 in the semi-final — still an Olympic record. When he later defended his doctoral thesis in mathematics, the audience reportedly contained more football fans than mathematicians.
Why it matters: Bohr went on to create the theory of almost periodic functions, a powerful generalization of periodic behavior that influences signal processing, differential equations, and number theory to this day. He was also the brother of Nobel Prize-winning physicist Niels Bohr — making them perhaps the most brilliant sibling duo in scientific history.
Did you know?
There's a shape called a Reuleaux triangle that has three curved sides and three pointy corners — yet it rolls as smoothly as a perfect circle. Even wilder: engineers use drill bits shaped like Reuleaux triangles to cut holes that are nearly perfect squares!
A Reuleaux triangle is constructed by drawing three circular arcs, each centered on one corner of an equilateral triangle and passing through the other two corners. This gives it a property called "constant width" — the distance between any two parallel lines squeezing the shape is always the same, just like a circle. When it rotates inside a square boundary, its corners trace a path that covers about 98.8% of the square's area, producing a nearly square hole.
Done?
- Solved the problem (or read through the steps)
- Read the history note
- Read the "did you know" fact