It’s that time again for a sunshine trip to the Caribbean. Plenty of Vitamin Sea. And Vitamin R.
I’m flying on Tuesday and will be away for just three weeks, or so.
..the reason I was thinking about trihexadecimal numbers under that palm tree on the coral sand in front of the crystal clear Caribbean Sea was because I was trying to calculate the change in sea-level if all the sea sponges were taken out.
So, my previous thinking on the beach (about trihexadecimal numbers and sea sponges) led me to the wonderful world of Menger Sponges, which is something that has a surface area that approaches infinity while at the same time its volume approaches zero. I made a few of these (working my way up to a Level-4).
So on this trip, I’m going to be thinking about something different – weird numbers and untouchable numbers, and seeing if I can find a practical use for them. And maybe use Excel to generate some.
The smallest weird number is 70 (if you add up all its divisors, you get 74, which is bigger than 70; no subset of the divisors adds to 70, so 70 is officially a weird number).
An untouchable number is a number that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). So 4998 is untouchable. But 4 isn’t (because the proper divisors of 9 happen to be 1 and 3, and 1 + 3 = 4, so 4 can be expressed as the sum of all the proper divisors of the number 9).
Looking forward to Happy Hour at 5
zeddy
(5 is believed to be the only odd untouchable number, but after a few rums, who knows…)
