#47 Geometra鈥檚 tomb
Long before the invention of satnav, the great explorer Asosa Lees embarked on a trek across the square desert of Angula in a quest to find the lost tomb of Geometra, which lay somewhere along the line marked A.
Lees had nothing but the crude and incomplete diagram shown and some basic instructions: proceed south-west for 100 kilometres, and then turn left. The only other information she had was that at the moment she turned left, the distance to the south-west corner of the desert was 100 kilometres further than the distance to the south-east corner.
To reach the tomb, Lees needed to head in precisely the right direction. Fortunately using her knowledge of geometry she was able to take the correct bearing. At what angle did she head off towards the tomb?
Answer next week
#46 Pi-thagoras
Solution
The area of the circle is 蟺, about 3.14. To determine that, draw three lines from the centre of the circle that meet the triangle鈥檚 sides at right angles. These lines are all the same length, that of the radius of the circle (r).
The length AB is 3 鈥� r, and by symmetry AC = 3 鈥� r. Similarly DE and CE both = 4 鈥� r.
Because AE = 5, then (3 鈥� r) + (4 鈥� r) = 5.
This can be rewritten as 7 鈥� 2r = 5.
So 2r must be 2, and r = 1.
The area of a circle is 蟺r2.
So this circle鈥檚 area is 蟺 脳 12, which is 蟺.
Quick quiz #39
1 Named for their ghostly ability to blend in with vegetation, insects of the order Phasmatodea are better known as what?
2 In 2000, scientists at the Brookhaven National Laboratory in the US collided gold atoms at near light speed to create what state of matter, thought to have existed in the first instants after the big bang?
3 Who is the only British woman so far to win a Nobel prize in physics, chemistry or medicine?
4 Which purple-coloured organ, found under the left side of the diaphragm, filters out old and damaged red blood cells from our blood?
5 Austrian mathematician Kurt G枚del is best known for which unsatisfying conclusion(s)?
Answers below
Quick quiz #39
Answers
1 Stick bugs or stick insects
2 A quark-gluon plasma
3 Dorothy Hodgkin. She won the 1964 Nobel prize in chemistry for using X-rays to discover the structures of biochemicals
4 The spleen
5 His incompleteness theorems, which seem to indicate that sets of axioms purporting to explain mathematics are fated always to have logical holes