MOTION MOUNTAIN

274 8 thought and language
⊳ Everything in nature is numbers.
But Pythagoras and his sect were wrong. Like for so many beliefs, observation will show
the opposite. We will discover this in the last part of our adventure.The assumption that
observations in nature can be separated is an approximation. In short:
⊳ Counting is an approximation.
Challenge 272 s
The foundations of physics we used so far are built on sand. A better foundation is
needed.The quoted ‘incomprehensibility’ of nature then becomes amazement at the precisionofthisapproximation.Thisexperienceisthehighpointofouradventure.
“DiePhysikistfürPhysiker vielzuschwer.*
DavidHilbert”
Curiosities and fun challenges about mathematics
What is the largest number that can be written with four digits of 2 and no other sign?
And with four 4s?
Pythagorean triplets are integers that obeya 2 +b 2 =c 2 . Give at least ten examples.Then
Challenge 273 e show the following three properties: at least one number in a triplet is a multiple of 3;
at least one number in a triplet is a multiple of 4; at least one number in a triplet is a
multiple of 5.
Challenge 274 e
Challenge 275 s
Challenge 276 d
Challenge 277 s
Challenge 278 s
∗∗
∗∗
How many zeroes are there at the end of1000! ?
∗∗
A mother is 21 years older than her child, and in 6 years the child will be 5 times younger
than the mother. Where is the father? This is theyoungmotherpuzzle.
∗∗
The number1/n, when written in decimal notation, has a periodic sequence of digits.
The period is at mostn−1 digits long, as for1/7=0.1428571428571428.... Which other
numbers1/n have periods of lengthn−1?
∗∗
Felix Klein was a famous professor of mathematics at Göttingen University. There were
two types of mathematicians in his department: those who did research on whatever
they wanted and those for which Klein provided the topic of research. To which type did
Klein belong?
Obviously, this is a variation of another famous puzzle. A barber shaves all those
people who do not shave themselves. Does the barber shave himself?
* ‘Physicsismuchtoodifficultforphysicists.’
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net