#47 Squares and circles
Set by Katie Steckles
A circle is drawn so it touches the sides of a square, and then the largest square that fits is drawn inside the circle.
What is the ratio between the area of the small square and large square? (Hint: you might find it useful to rotate the inner square.)
Consider the larger square and the circle. How many copies of the circle do you need to completely cover the square?
With a nod to the late mathematician David Singmaster, who wrote a paper based on this problem: which fits better 鈥� a square peg in a round hole, or a round peg in a square hole? (By 鈥渇its better鈥�, we mean a larger proportion of the hole is taken up by the peg.)
Solution next week
#46 OhmWork
Solution
These are the three other possible circuits using three 1-ohm resistors. Their overall resistances are 1/3, 2/3 and 3 ohms:
The circuit described, made of 10 1-ohm resistors, has a resistance of 22/7 ohms (approximately 蟺).
The unique (except for equivalent rearrangements) circuit achieving 22/7 ohms with nine 1-ohm resistors looks like this:
Quick quiz #279
set by Bethan Ackerley
1 Tau particles have what value of spin?
2 Zoozve is a quasi-moon of which planet in the solar system?
3 Edaphology and pedology are branches of the study of what substance?
4 Rickettsia prowazekii is a bacterial species behind which disease?
5 Ayn Ghazal is a Neolithic site in which modern-day country?
Quick quiz #279
Answers
1 1/2
2 Venus
3 Soil
4 Typhus, more specifically epidemic typhus
5 Jordan