Year 1989- Volume 25
2020 - Present

William Taylor

The popularity of the special theory of relativity stems from extraordinary predictions about time, distance, mass, Energy and the nature of space.

Bob Hart

About 1637 Pierre Fermat wrote the following famous note in the margin of Bachet's translation of Diophantus' Arithmetica:

Albert Daoud

The equation $\int f\left(x\right)dx=F\left(x\right)+C$ where $f\left(x\right)dx=F\left(x\right)+C$ is familiar to us when studying integration.

Q.753 When multiplying two whole numbers a student by mistake reduced the tens digit in the answer by 7.

Q.762 Simply the sum

$\mathrm{sec}\left(\theta \right)+\mathrm{sec}\left(\theta \right)\mathrm{sec}\left(2\theta \right)+\mathrm{sec}\left(2\theta \right)\mathrm{sec}\left(3\theta \right)+\cdots +\mathrm{sec}\left(\left(n-1\right)\theta \right)\mathrm{sec}\left(n\theta \right)$

Helen Martin

One of the most difficult problems actuaries face is learning how to answer the question "What do you do?". Unfortunately there is no short answer.

Werner Ricker

Recall that a real number is called rational if it can be expressed in the form $p/q$ where $p$ and $q$ are integers with $q\ne 0.$

David Tacon

Historians seem to generally agree that the first appearance of something which is recognizably civilization occurred in the southern part of Mesopotamia about 5000 years ago.

$a$ and $b$ are positive integers. Of the following statements, three are true, one is false.

Q.762 Simply the sum

$\mathrm{sec}\left(\theta \right)+\mathrm{sec}\left(\theta \right)\mathrm{sec}\left(2\theta \right)+\mathrm{sec}\left(2\theta \right)\mathrm{sec}\left(3\theta \right)+\cdots +\mathrm{sec}\left(\left(n-1\right)\theta \right)\mathrm{sec}\left(n\theta \right)$

Q.773 Prove that t$\mathrm{tan}\left({36}^{\circ }\right)×\mathrm{tan}\left({72}^{\circ }\right)=\sqrt{5}.$

Bruce Harris

Actuaries may be regarded as highly trained business mathematicians.

Esther Szekeres

Physics and mathematics have interacted with each other in the course of centuries, each enriching the development of the other.

Peter Petocz

Q.782 Let ${S}_{n}=\frac{1}{{1}^{2}-\frac{1}{4}}+\frac{1}{{2}^{2}-\frac{1}{4}}+\frac{1}{{3}^{2}-\frac{1}{4}}+\cdots +\frac{1}{{n}^{2}-\frac{1}{4}}$. Simply this expression, and show that $n$${}_{}$
is large ${S}_{n}$ is approximately equal to 2.
Q.773 Prove that  $\mathrm{tan}\left({36}^{\circ }\right)×\mathrm{tan}\left({72}^{\circ }\right)=\sqrt{5}.$