Zero x Infinity

WHAT’S ZERO TIMES BY INFINITY? 

SHORT ANSWER: 0 x ∞ = anything you like! Intrigued? Read on… LONG ANSWER: the question seems absurd: after all, zero multiplied by anything is zero, yet any multiple of infinity is always infinity. But 0 x ∞ cannot be both zero and infinity, can it? Infinity doesn’t behave in the same way as other

the Greatest Mistake of Maths

THE GREATEST MISTAKE IN THE HISTORY OF MATHS: 

This must surely be the exclusion of women from maths for most of our history, due to mathematics (and academia in general) being seen as an unsuitable activity or as simply “too hard” for women. As we see the female:male ratio among the best brains of mathematics now approaching 1:1, one wonders how much more

Measuring a Diabolo High Throw

USING MATHS TO CHECK WORLD RECORD ATTEMPTS: PETE’S DIABOLO HIGH THROW 

My friend Pete can throw a diabolo ridiculously high – check out this video of him in action! Pete thinks his throw is higher than the “official” world record of 23.92metres so asked me if maths could measure his throw. So, how about it, maths? METHOD 1 (not recommended!): get a long tape measure and

Hippasus

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

Irrational Numbers

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

angles in a triangle equal 180 degrees

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“).

Zero

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:

Venn Shapes Puzzle

PUZZLE OF THE WEEK 

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

Gradient of world's steepest road

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

Type Maths Symbols

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?

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

Quotation: God made the integers, all else is the work of man

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,