HIPPASUS

HIPPASUS: was an Italian born mathematician who lived around 500BC. Legend has it that Hippasus was drowned at sea after daring to suggest that some numbers cannot be written as one whole number divided by another. His pals at the Pythagorean school of maths clearly thought this idea was shocking – but it turns out

Strange but True: IRRATIONAL NUMBERS

The first numbers we discover in childhood are the Natural Numbers: 1, 2, 3, … Next come the Integers (whole numbers) – which also include Zero and the negatives: … -3, -2, -1, 0, 1, 2, 3, … Next up: it’s fractions such as: 0.5, 2.90909… , $-\Large{5}\frac{7}{8}$ Numbers like these are said to be

WHY THE ANGLES IN A TRIANGLE ADD TO 180°

Given any triangle: Rotate so that the longest side lies horizontally along the base. Extend the base, and draw a parallel line going through the uppermost corner (these two lines are shown in light blue). The two red angles are the same size (using the well-known “parallel lines” angle result alternate angles, sometimes called “Z-angles“).

What’s special about ZERO?

(or: Much ado about Nothing) Zero doesn’t actually exist. Think about it: by definition it isn’t anything, it’s nothing!! Even so, here are 5 facts every mathematician should know about Zero:

PUZZLE OF THE WEEK

What shape goes in the intersection of this Venn Diagram? Read on for the answer:

HOW DO GRADIENTS WORK?

Here I am at the World’s Steepest Road in Harlech, North Wales. The road sign indicates an almighty 40% – but how is this measured? ON ROADS: The 40% means that however far you travel horizontally, you travel 40% of that vertically. So if you go 100m across, you go 40m up. SO A ROAD

5 WAYS TO TYPE SYMBOLS π λ √∫≤∑≈

not to mention $\frac{e^{-t}}{y^3+1}$ To type Mathematical Symbols on your PC: 1) USE WINDOWS EMOJIS: To type ⅷ∀√∛∞∑²³ⁿ∃∞∫≈≡≥ and many more. Simply press windows key together with . to bring up the emoji keyboard, then select Ω or ∞to bring up the maths palette. VERDICT: works with any app on PC including Facebook, Twitter, MS

WHICH ARE BETTER: FRACTIONS OR DECIMALS?

DECIMALS ARE WAAAY BETTER THAN FRACTIONS: most GCSE students prefer decimals because they allow you to compare the sizes of two numbers at a glance! For instance, which is bigger out of $\frac{2}{5}$ and $\frac{3}{7}$? Um…? But in decimal form we can easily see that $\frac{3}{7}=0.428571…>0.4=\frac{2}{5}$. FRACTIONS RULE SUPREME: fractions allow for easy multiplication, and

QUOTE OF THE WEEK: “God Made the Integers. All Else is the Work of Man”

… or so thought Leopold Kronecker (1823-1891) in his famous quote. WHY KRONECKER WAS WRONG: the integers (whole numbers) include the Positive Integers or “counting numbers” 1, 2, 3, 4 and so on: easy for a child to understand. We could quite reasonably argue they are “made by God”. But the integers also include zero,

HYPOTHESIS TESTS

In statistics, these wonderful techniques allow us to use some data that we have collected to make predictions and conclusions about the real world. AN EXAMPLE: Amy and Bill are playing snakes and ladders, but Amy thinks Bill is cheating because he keeps rolling a six. Bill insists he is just being lucky. They decide

FACTORIALS!

Factorials are so cool that the notation is: AN EXCLAMATION MARK!!!! The exclamation mark means something very specific in maths. It’s great to be impressed with numbers, but please do not put an exclamation mark after a number just to show that it’s really cool. WHAT IS IT? n Factorial (written $n!$) means the product

WORD OF THE WEEK: INDEX

INDEX (plural indices): you can see these in expressions like $5^2 = 25$. The 5 is called the BASE, the 2 is called the EXPONENT or INDEX, and the 25 is called a power (in this case it’s a power of 5).