素数の星空の中から星座を探せ！ #日曜数学会
TRANSCRIPT
Constellations in the Gaussian primes
@tsujimotter
http://tsujimotter.info/
# 2016/06/18
Who are you
tsujimotter
Terrence Tao, “The Gaussian Primes Contain Arbitrarily Shaped Constellations”,
arXiv:math/0501314 [math.CO]
http://arxiv.org/abs/math/0501314
Z[ i ] (Shape)
P[ i ]
(Constellation)
1.2
“ ”
i
2i
3i
-i
-2i
-3i
-1 0 1 2 3 4 5
“ ”
-1 0 1 2 3 4 5
-1 0 1 2 3 4 5
“ ”
-1 0 1 2 3 4 5
i
2i
3i
-i
-2i
-3i
5 + 2i
7
3i {1, -1, i, -i } {p, -p, pi, -pi}
p
{1, -1} {p, -p}
p
5+0i-5+0i
0+5i
0-5i
5 + 2i
3i
100+0i-100+0i
0+100i
0-100i
300+0i-300+0i
0+300i
0-300i
Z[ i ] (Shape)
P[ i ]
(Constellation)
1.2
Shape
Shape Constellation
+30
-30
- 5 - 2i - 1 - 4i 1 - 6i 3 - 8i
3 - 10i 7 - 12i 9 - 10i
+100
-100
-70 + 71i 10 + 61i - 10 - 9i
- 20 - 19i - 30 - 29i 30 - 89i
- 50 - 99i
4/21 5/20
+50
-50
-30 + 23i -38 + 7i -2 + 3i 2 - 1i 2 - 5i
- 2 - 5i - 6 - 5i
6
8
10
+300
-300
5/21 6/21
+50
-50
-38 + 23i -44 + 15i -16 + 9i -6 + 5i -2 + 5i
-32 + 3i -26 + 1i - 12 - 7i
{ -30 + 23i, -38 + 7i, -2 + 3i,
2 - 1i, 2 - 5i, - 2 - 5i, - 6 - 5i }
❤
8/24 9/23
+30
-30
-13 + 2i 7 - 2i
- 11 - 6i 7 - 8i
- 21 - 10i - 7 - 10i - 1 - 10i
- 15 - 14i - 19 - 20i
+1200
-1200
http://tsujimotter.info/works/constellation/