Denys Fisher sale in Schofields department store in Leeds in 1965. A year later, Fisher licensed Spirograph to Kenner Products in the United States. In 1967 Spirograph was chosen as the UK Toy of the Year. Denys Fisher Toys, which also produced other toys and board games, was sold to Palitoy in 1970 and it was subsequently bought by Hasbro. Through the 1980s & 1990s Fisher continued to work with Hasbro in developing new toys and refining Spirograph. Denys Fisher Toys produced the following toys and games: Denys Fisher Denys Fisher (11 May 1918 – 17 September 2002) was an English engineer
Inequality of arithmetic and geometric means numbers in the case . An example of this case is : Averaging two different numbers produces two equal numbers, but the third one is still different. Therefore, we never actually get an inequality involving the geometric mean of three equal numbers. Hence, an additional trick or a modified argument is necessary to turn the above idea into a valid proof for the case . With the arithmetic mean of the non-negative real numbers , the AM–GM statement is equivalent to with equality if and only if for all . For the following proof we apply mathematical induction and only