The reaction in Fig.1 takes place rapidly when manganese(IV) oxide is present in the mixture. However, the manganese(IV) oxide is unchanged when the reaction has finished: it acts as a catalyst. At the end of this reaction, when all the hydrogen peroxide has broken down, the catalyst remains chemically unchanged.
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Perfect number. Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.