Gems From the Exeter Math Books

Some real "what the heck" moments from Exeter Math: Math 3, pg 52 3. Imagine covering an unlimited plane surface with a single layer of pennies, arranged so that each penny touches six others tangentially. What percentage of the plane is covered? WTH METER: **TIME SPENT TRYING: ***** Math 4, pg 98 7. A cylindrical water glass is filled with water and then tilted until the remaining water covers exactly half the bottom of the cylinder. What fractional part of the water remains? WTH METER: ****TIME SPENT TRYING: *** Math 2, pg 48 10. The Doppler Shift. While driving a car, AJ honks the horn every 5 seconds. Hitch is standing by the side of the road, and hears the honks of the oncoming car every 4.6 seconds. The speed of sound is 330 meters per second. Calculate the speed of AJ’s car. Describe what Hitch hears after the car passes. WTH METER: *****TIME SPENT TRYING: nul Math 1-4, pg Pick One 7. Alex the Geologist has mistakenly found herself in the middle of the cold, barren wasteland of outer space. Discovering that space actually has very little rocks, she decides to come back to the desert. However, Alex the Geologist is not only running low on oxygen, she’s also really thirsty, and wants an ice cold Coke. Assuming Alex must stop at the nearest Chinese restaurant to pick up dinner (remember that the Earth is spinning), how long will it take her to get stuck somewhere dangerously far from civilization again? WTH METER: *****TIME SPENT TRYING: solve by 2020