50 Mathematical Ideas You Really Need to Know

When applying this conversion recipe to other fractions it is possible that we might never finish! We could keep going forever; ...

hieroglyphs designating unit fractions – those fractions whose numerators are 1. We know this from the Rhind Papyrus which is ke ...

04 Squares and square roots If you like making squares with dots, your thought patterns are similar to those of the Pythagoreans ...

number 36 appears in both lists. But there is a more striking link. If you take successive triangular numbers and add them toget ...

reflected signals when parallel beams from space hit the curved dish and bounce towards the focus point. In a car headlight a li ...

These numbers all have square roots, but they are not equal to whole numbers. Virtually all calculators have a √ button, and usi ...

unit would fit flush with the end-point of the mth AB. The length of AB would then be m/n. For example if 3 copies of AB are lai ...

We can assume that m and n have no common factors. This is OK because if they did have common factors these could be cancelled b ...

05 is the most famous number in mathematics. Forget all the other constants of nature, π will always come at the top of the li ...

of buoyancy in hydrostatics? How he celebrated his work on π is not recorded. Given that π is defined as the ratio of its circum ...

circle is. πr 2. Archimedes estimated the value of π as bounded between and. And so it is to Archimedes that we owe the familiar ...

Lindemann concluded the problem of ‘squaring the circle’. Given a circle the challenge was to construct a square of the same are ...

The letter count of each successive word in Keith’s version provides the first 740 digits of π. The importance of π What is the ...

06 e e is the new kid on the block when compared with its only rival π. While π is more august and has a grand past dating back ...

may not seem much but if we had £10,000 to invest, we would have £2,250 interest instead of £2,000. By compounding every half-ye ...

top and bottom are limited to three-digit numbers the best fraction is 878/323. This second fraction is a sort of palindromic ex ...

close but it is easily shown (without actually calculating their values) that eπ > πe. If you ‘cheat’ and have a look on your ...

An earth-shattering identity The prize for the most remarkable formula of all mathematics involves e. When we think of the famou ...

07 Infinity How big is infinity? The short answer is that ∞ (the symbol for infinity) is very big. Think of a straight line with ...

probably something like ‘half the whole numbers are odd and half are even’. Cantor would agree with the answer, but would give ...