#46 Pi-thagoras
Pythagoras鈥檚 theorem says that for any right-angled triangle, the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides.
There are some right-angled triangles whose sides are all whole number lengths. The simplest and best known is the 鈥�3-4-5鈥� triangle (32 + 42 = 52).
I have drawn a circle that fits precisely inside a 3-4-5 triangle. What is the area of the circle? Have a guess. And then see if you can prove that you are right.
Answer next week
#45 Beetles on a clothes line
Solution
The last two beetles to drop off the line, both after 2 minutes, are beetle B at the left-hand end and beetle C at the right-hand end.
When two beetles meet, they reverse direction. But blur your eyes and you may see that this is equivalent to the two beetles walking past each other on parallel paths.
So, a beetle that starts at one end will walk 2 metres (taking 2 minutes) before dropping off the opposite end. Four beetles are pointing to the right at the start, so we will see four of them drop off the right-hand end, and since beetles can鈥檛 actually go past each other, the beetle that starts four places from the right (beetle C) must be the last one that drops off the right-hand end.
By the same reasoning, two beetles fall off to the left, the second of these being beetle B.
Quick quiz #38
1 Based on their different neurobiology, lust, attraction and attachment are the three main subcategories of what?
2 Which of the three is thought to be principally mediated by the hormones dopamine, norepinephrine and serotonin?
3 Also known as the 鈥渃uddle hormone鈥�, which peptide hormone plays a major part in social and reproductive attachment in many mammal species?
4 The medication sildenafil, sold under the brand name Viagra among others, was originally developed as a treatment for what?
5 During the mating season, what accounts for up to 63 per cent of a female praying mantis鈥檚 diet, according to a 2016 study?
Answers below
Quick quiz #38
Answers
1 Love
2 Sexual attraction
3 Oxytocin
4 Heart-related chest pain, or angina
5 Male praying mantises