Comments by "zenith parsec" (@zenithparsec) on "Mathologer" channel.

  1. The version of the t-shirt in the zazzle link you gave in the description is bad. it ruins the joke completely by not using the custom font Y. So where did you REALLY get the t-shirt? Please let us support artists who actually understand what they are putting on the shirts.
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  2. tl;dr? All primes up to a million gets within 0.0000001 of pi. So I tried the approximation like you suggested, using bash because I couldn't find my pencil. $ echo {1..100} | xargs -n10000 factor | grep -E '^(.+): \1' | cut -f1 -d: | tr '\n' ' ' > primes # make a file with all the primes up to 100. $ wc -l primes # how many primes in the file? 25 primes $ { echo -ne 'scale=100;\n define n(x) { xx= x * x; rxx = 1/xx; return 1-rxx; }\n sqrt(6 / ('; printf 'n(%s) *' `cat primes ` ; echo ' 1 ))'; } | bc 3.138737195071720955523189928777768051930643408355181706902928964122\ 6073228989631725449338588507152448 Not terrible, I guess. 3.138 is almost 3.14159256... But, using a few (ok, a lot) more primes... $ echo {1..1000000} | xargs -n10000 factor | grep -E '^(.+): \1' | cut -f1 -d: > primes $ wc -l primes # how many primes in the bigger file? 78498 primes $ # this time I also compare against pi calculated by arctan(1) * 4: spoiler: it comes pretty close. $ { echo -ne 'scale=100;\n define n(x) { xx= x * x; rxx = 1/xx; return 1-rxx; }\nans=sqrt(6 / ('; printf 'n(%s) *' `cat primes ` ; echo ' 1 )); pi=a(1)*4; print ans,"\n",pi-ans,"\n"'; } | bc -l 3.141592547127987979164816081001222684451736462979299582954285924973\ 1246992477303058113590016970323364 .0000001064618052592978273022782801997454329363958062380206586673346\ 917070384786928166758236450847312
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  3. Please give a pause so I don't have to run up and press pause to spot the pattern. Some of us are in the middle of winter sitting wrapped in blankets, so it can take a few seconds to get up. But I got it before continuing in a minute or so. (difference between the two columns is one less than two up.
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  4. "Can you write the numbers 2 and 3 as sums of distinct positive integers?" It really depends on what you mean by 'write'... For 3, [edit] 1/1+ 1/2+ 1/3+ 1/4+ 1/5+ 1/6+ 1/7+ 1/8+ 1/9+ 1/10+ 1/15+ 1/230+ 1/57960 The sum of the reciprocal of all powers of 2 of positive integers sums to 2.... 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + 1/2048 + 1/4096 + 1/8192 + 1/16384 + 1/32768 + 1/65536 + 1/131072 + 1/262144 + 1/524288 + 1/1048576 + 1/2097152 + 1/4194304 + 1/8388608 + 1/16777216 + 1/33554432 + 1/67108864 + 1/134217728 + 1/268435456 + 1/536870912 + 1/1073741824 + 1/2147483648 + 1/4294967296 + 1/8589934592 + 1/17179869184 + 1/34359738368 + 1/68719476736 + 1/137438953472 + 1/274877906944 + 1/549755813888 + 1/1099511627776 + 1/2199023255552 + 1/4398046511104 + 1/8796093022208 + 1/17592186044416 + 1/35184372088832 + 1/70368744177664 + 1/140737488355328 + 1/281474976710656 + 1/562949953421312 + 1/1125899906842624 + 1/2251799813685248 + 1/4503599627370496 + 1/9007199254740992 + 1/18014398509481984 + 1/36028797018963968 + 1/72057594037927936 + 1/144115188075855872 + 1/288230376151711744 + 1/576460752303423488 + 1/1152921504606846976 + 1/2305843009213693952 + 1/4611686018427387904 + 1/9223372036854775808 + 1/18446744073709551616 + 1/36893488147419103232 + 1/73786976294838206464 + 1/147573952589676412928 + 1/295147905179352825856 + 1/590295810358705651712 + 1/1180591620717411303424 + 1/2361183241434822606848 + 1/4722366482869645213696 + 1/9444732965739290427392 + 1/18889465931478580854784 + 1/37778931862957161709568 + 1/75557863725914323419136 + 1/151115727451828646838272 + 1/302231454903657293676544 + 1/604462909807314587353088 + 1/1208925819614629174706176 + 1/2417851639229258349412352 + 1/4835703278458516698824704 + 1/9671406556917033397649408 + 1/19342813113834066795298816 + 1/38685626227668133590597632 + 1/77371252455336267181195264 + 1/154742504910672534362390528 + 1/309485009821345068724781056 + 1/618970019642690137449562112 + um... I'm going to run out of space, aren't I? now @ 31:52 ... So it looks like I wasn't cheating. and trivial way to represent so here's 4: 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/200 + 1/77706 + 1/16532869712 + 1/3230579689970657935732 + 1/36802906522516375115639735990520502954652700 + 1/1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (Replace each ! in that with 1000 zeros, and you get an answer which is accurate to 112120 digits. (Today is 11/21/20, which is why i used that number.) the 'bc' code to get that answer: ms=112120; scale=ms; s=0; for(i = 1; s < 4-(1/10^(scale )); ) { r=1/i; i=i+1; if(s+r < 4) { s=s+r; print "1/",i-1 ," + "; if(s < 4 && s > 4- (1/i) ) { scale=0; i = 1/(4-s); scale=ms; }; }; }; print "\n";
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