1912 (23 June): Birth, Paddington, London

1926-31: Sherborne School

1930: Death of friend Christopher Morcom

1931-34: Undergraduate at King's College, Cambridge University

1932-35: Quantum mechanics, probability, logic. Fellow of King's College, Cambridge

1936: The Turing machine, computability, universal machine

1936-38: Princeton University. Logic, algebra, number theory

1938-39: Return to Cambridge. Introduced to German Enigma cipher machine

1939-40: The Bombe, machine for Enigma decryption

1939-42: Breaking of U-boat Enigma, saving battle of the Atlantic

1943-45: Chief Anglo-American crypto consultant. Electronic work.

1945: National Physical Laboratory, London

1946: Computer and software design leading the world.

1947-48: Programming, neural nets, and artificial intelligence

1948: Manchester University, first serious mathematical use of a computer

1950: The Turing Test for machine intelligence

1951: Elected FRS. Non-linear theory of biological growth

1952: Arrested as a homosexual, loss of security clearance

1953-54: Unfinished work in biology and physics

1954 (7 June): Death (suicide) by cyanide poisoning, Wilmslow, Cheshire.

Alan Turing in 1946.

Full picture

My publications: Many on-line papers including a short overview biography of Alan Turing. Complete listing .

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(10h) Do not act the Good Samaritan to blacks in apparent distress, ., on the highway.

First, we need to find the area of the trapezoid by using the area formula
of the trapezoid.

A=(1/2)h(b1+b2) area of a trapezoid

In the above diagram, h=a+b, b1=a, and b2=b.

A=(1/2)(a+b)(a+b)

=(1/2)(a^2+2ab+b^2).

Now, let's find the area of the trapezoid by summing the area of the three
right triangles.

The area of the yellow triangle is

A=1/2(ba).

The area of the red triangle is

A=1/2(c^2).

The area of the blue triangle is

A= 1/2(ab).

The sum of the area of the triangles is

1/2(ba) + 1/2(c^2) + 1/2(ab) = 1/2(ba + c^2 + ab) = 1/2(2ab + c^2).

Since, this area is equal to the area of the trapezoid we have the following
relation:

(1/2)(a^2 + 2ab + b^2) = (1/2)(2ab + c^2).

Multiplying both sides by 2 and subtracting 2ab from both sides we get

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