In Mathematics
Its factorization makes it a sphenic number. 70 is a Pell number and a generalized heptagonal number, one of only two numbers to be both. Also, it is the seventh pentagonal number and the fourth 13-gonal number, as well as the fifth pentatope number. It is the smallest weird number.
The sum of the first twenty four squares starting from one is seventy squared. This relates seventy to the Leech lattice and thus string theory.
Since it is possible to find sequences of 70 consecutive integers such that each inner member shares a factor with either the first or the last member, 70 is an Erdős–Woods number.
In base 10, it is a Harshad number.
Read more about this topic: 70 (number)
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“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)