证明: [tex=5.357x2.143]ShkXE4XX5myJ7aKwW8FZx63JkMbh3NrsyxJvMWrP/bcUTYvSgBVsy1S/k84SFzEE[/tex]是极小曲面.并求它的主曲率.

2022-06-15

证明: [tex=5.357x2.143]ShkXE4XX5myJ7aKwW8FZx63JkMbh3NrsyxJvMWrP/bcUTYvSgBVsy1S/k84SFzEE[/tex]是极小曲面.并求它的主曲率.

答案：

证明：[tex=8.643x2.214]rKDHBLxB4zCdKivfV7E1tFg7UfdnEp+Te6srdueIOEsxMBq7qkVtYkTfyE23yrqrACj8NxL1sU8QiTps7fT13xzNVB4cglElcCcHbQDqQ7E=[/tex],  [tex=9.0x2.786]ZYm/iRSkqT1w/CHmC4hRHSRPBvDaK2P5HY3rVlWp0w8eMOX7XQJUgkVMsJBobbWESEEPQAjVSLeg1PhJgUNXQQ==[/tex], [tex=8.143x2.786]fAFrdRtEzQNLrmkRojULYSOWAbxDScl+C4l1OExwZ2YlLtjRn1B0shh8ny8Ez0Mh2LCmaR/E9Wi+jC019CbKmg==[/tex] [tex=19.214x3.429]tSmrAvz3zGXUIh9mqGyQoXDbcfO7P5rEqraJNeSQK0wmL+tW1GWVshmcDszstL/5Bf41OMN1PR6u3+wTxdlblVSUcFyI0xaQqHxXS9RvN/1vqAgZwkMxikJb+gVDMhrzCL4Sf57zVsHzygw+2CBjrg==[/tex] [tex=9.786x2.857]RXziKGu7BCQOHBr4YkrUHivX8rjN//fT2C9Bh3XCqSm2hmFX6L4YGfjY9rdfZutokwOJgGFgDrsDqC98A+WF+MmVoP/uyNUw2VMjlFNFHQk=[/tex], [tex=10.143x3.357]OjMvrqB5X1ReiqMUuphmltCmIXOABaTpljcLYpWKzCEoa7QyIgqT2dmWLG7kHbseH/UpASQD9VdeXUQQkzM5hguApFUOHG/z2og0isIHlOPHGmudddlmH/tBZOJTLNdq[/tex], [tex=9.643x2.857]ky1/yUggZDyVZqSoHcH/Sp+f1mfvH8SAvh5RW6n7gYK3Zp7MSdLU7U7mkI9VSiy0dGo4elf9Ok4h6JjTqLOMjGN8Tsvv+A0qkGxpWL4CUF4=[/tex][tex=8.0x2.857]rxOAX6t4+aI5AAKvuhj0bx0RMIRNgeXdmJ7vEhs3HGFwfzrlTZCm2mCrunVrADV6rNPqn30nV8xdD8b2B36oLA==[/tex], [tex=6.429x2.857]EmTiKyCU/GAP85u9vO8Xf33E8pM9JVTRzrxD7Nhoa83J0703/+f5E3Vxnzsstselt0Tc7x9Il+cZlqlwiniRhA==[/tex], [tex=7.071x2.857]71cPqpepqs8fMEyboZnEQb4YjHDH1Q7k2saI/XmQiKmfsUo23V7xY7M3ExVmJNIlOEwzflxaYx5jKzFXDrbJIA==[/tex][tex=15.571x3.429]MfzbxhdHU7qpo8VrqUxMAWNqRtOcIkmgprN+aOGtZG/8d+y77+KCSxKZwb7MtksIOrCohmQTeJgLv7Fby4lnCJ8c82Dw5msWsRUzcZTcrGxx6I0xM1RoO7m0ICJ/akL+cYSn8qZ456mSqa7qmwprDQ==[/tex][tex=15.857x3.714]h3PwaRu6AJFeSaSPRdOe2MlwG5I5tu0VPSpjoSw7hJ200ZIs4XGZYqy+jQcrLwK/x+yjQ7uyZVvTdYG4eUhlyiEem+3qK4sH0l3ByawbavOU5QrLARrNNdzLLsTSq5c2DBeVvSHggUc+ESjWkLOBZtTnIheFrEToonrhaJFrVQI=[/tex][tex=15.714x3.429]e93ysjYz7jGzhTrVVXpDnG/zhi7Is7TswLOcAmwo1mW2ajroDWkyYKKty6ucfnuEy5P4gnYEYMcXaDbVvL+X00XnjGv9/exSu1pwmgZDKROL3XEZruMcXj8kDD83+AHxZsgrcZ1i+UpCS+krtEa1Xw==[/tex]故[tex=8.0x1.143]ZS0FHv++x7n4d7GepoDWRxfkxC2a5O6O6YebfrE5jIQ=[/tex], 从而[tex=2.143x1.0]06D+f+qmGa17tGNcaZ4lsQ==[/tex], 即曲面为极小曲面.又[tex=17.714x2.857]6ZT7pJQCynOizOTheEYPP7aFex8Vl6RMOMeHowH0B/FK59CGtudOFKCV7tJjwRowAEz9TXQTG3gMhzmhLJ4Qf6V8jiA+FFXUyh/4eHD5JOUGq/6rKhkehmYsRU2eulj/VDCE/a7ecUM6P1tETCbK8g==[/tex]故[tex=6.357x2.357]8qky71vtpCxx0E50hdHuWi2M3q1awanupdsDpz7rBx1LTYhkqsueW1PEVvPypkLe[/tex], [tex=7.143x2.357]JrOM0p0R4PRBBdHbFKycdrnQRcYumbbquHzsuTyFkWKziE/lsv7VDHBCfoHCTj0/[/tex].

举一反三

内容

0
输出九九乘法表。 1 2 3 4 5 6 7 8 9 --------------------------------------------------------------------- 1*1=1 2*1=2 2*2=4 3*1=3 3*2=6 3*3=9 4*1=4 4*2=8 4*3=12 4*4=16 5*1=5 5*2=10 5*3=15 5*4=20 5*5=25 6*1=6 6*2=12 6*3=18 6*4=24 6*5=30 6*6=36 7*1=7 7*2=14 7*3=21 7*4=28 7*5=35 7*6=42 7*7=49 8*1=8 8*2=16 8*3=24 8*4=32 8*5=40 8*6=48 8*7=56 8*8=64 9*1=9 9*2=18 9*3=27 9*4=36 9*5=45 9*6=54 9*7=63 9*8=72 9*9=81
1
求曲面[tex=4.857x1.357]yAyGqmPH6uVjsoklyRFjPsCn4ES71/IKAdIjF9MTDysk+Tc3QH5+wOsYsSqrGOMG[/tex]的[tex=2.857x1.0]nFfMk1gAq4fR5TwPu+p8Og==[/tex]曲率,并指出稍圆点和双曲点的区域.
2
输出九九乘法表。 123456789 --------------------------------------------------------------------- 1*1=1 2*1=22*2=4 3*1=33*2=63*3=9 4*1=44*2=84*3=124*4=16 5*1=55*2=105*3=155*4=205*5=25 6*1=66*2=126*3=186*4=246*5=306*6=36 7*1=77*2=147*3=217*4=287*5=357*6=427*7=49 8*1=88*2=168*3=248*4=328*5=408*6=488*7=568*8=64 9*1=99*2=189*3=279*4=369*5=459*6=549*7=639*8=729*9=81
3
输出九九乘法表。1 2 3 4 5 6 7 8 9---------------...9*7=63 9*8=72 9*9=81
4
s=1/(1*3)-1/(3*5)+1/(5*7)-1/(7*9)+......-1/(99*101)，编程求s的值并输出