The Last Song

My first day in Henderson,

Algebraic manipulation.

Thank You my Math teachers,

Had fun on my adventures.

Every day I learnt something new,

My brain, unfortunately, remembered few.

All the formulae make my brain jam,

To be honest, I want to remember them.

I know all of you care,

Concerned about how I fare.

Study hard I will,

Into the world I set sail.

So much memories I hold dear,

For all the years I have spent here.

Until the next reunion,

Never will we forget Henderson.

The Power of Power Functions

Recently, we came across this simple explanation by a Singaporean lady. It highlights that we should be aware of how quickly the Aedes mosquitoes are being bred. Hence, we should not be complacent about the measures that the government has done and do our part as well, to reduce and ultimately prevent the spread of Zika.

Here's the gist of it all:

You should know that the female Aedes mosquitoes are the ones guilty of spreading the virus as females need to feed on our blood for protein. An female mosquito infected with Aedes will lay eggs that contain the virus.

1) In her 5 weeks lifespan, a female Aedes mosquitoes lays about 300 eggs per week.

2) Considering that half of these eggs turn out to be female mosquitoes, we get 150 new born female Aedes mosquitoes.

3) Here comes the power of exponential! If each new born female Aedes mosquito go on to lay their own eggs, this is how many eggs we will get in just a short span of 5 weeks!

Week 1 - 1 Female Aedes mosquito
Week 2 - 150 eggs
Week 3 - 150^2 = 22500 eggs
Week 4 - 22500^2 = 3,375,000 eggs
Week 5 - 506,250,000 eggs

That's 506 million female Aedes mosquitoes waiting to break out from their egg and flying off to feed on our blood for protein. Just a simple power function of y = x^2 result in such a scary thought isn't it? 

This does not stop here according to this Singaporean lady. But to spare you guys from the scary findings done by the lady, we will link you the article here and stop talking about it now.

The findings done by this Singaporean lady is just a simple illustration on how quickly a power increases the original value. Before ending, do take note not to confuse power functions with exponential functions as they are quite different! (Location of x.) To read more about it, click here.

Finally, let's stay calm and focus on working together as a nation to reduce and ultimately prevent the spread of Zika.

Revision Tips Just For Math!

So we're approaching the final leg of our 2016 academic year. End of years is approaching, have you started revising?

#TRUTH

Here are some tips from your friendly Math teachers at Henderson:

1) ALWAYS PRACTICE. PRACTICE KEEPS YOU CALM.

Math is all about practicing. The more you practice, the more familiar you are with it, especially if you are those whose brain blanks out the moment you flip open the exam paper. Start by looking through past year papers, then move on to topical revision papers that your teachers have given you during Math class. Do the paper again, redo it once, twice and thrice. Remember, PRACTICE.

2) REMEMBER, REMEMBER, REMEMBER.

The formulas not provided in the formula sheet means you HAVE TO remember them! Formulas like TOACAHSOH, Pythagoras, Laws of indices, Coordinate Geometry and a few others... Remember them and if you are afraid that it will slip your mind, write it down immediately when the examiner says "Please begin." Even better, by PRACTICING, you will naturally REMEMBER. (Refer to point one.) Trust us.

3) ASK AND YOU SHALL BE GIVEN.

If you need help, get it. From your peers, teachers, and even the internet! Youtube has several channels teaching you how to solve Math problems. Channels like HegartyMath, Jayates and KhanAcademy. Listening to someone explain and talk through the approach and method used to solve a question often bring the clarification required for you to pursue similar questions yourself. 

4) KEEP CALM AND JUST DO IT.

Lastly, during the actual exam, many of you get flustered upon seeing a difficult question. NOT TO WORRY. Move on, and look for a manageable question to work through first. Gain confidence and then take on the more challenging questions. Do as much as you can in the stipulated time. Even when your answer might be wrong, SHOW YOUR WORKINGS (as the bulk of your grade comes from method marks). When you're done, CHECK YOUR WORK - check that you have typed everything accurately into the calculator, check that you have written everything correctly from the first line to the next, and check that you have ATTEMPTED EVERY SINGLE QUESTION. 

With a little luck and A LOT OF EFFORT...

Happy Numbers

This post is bound to put a big smile on your face. Why? Because we are going to talk about HAPPY NUMBERS!!

So what are happy numbers?
1) Start with a positive integer [e.g. 23]
2) Replace the number by the sum of the squares of its digits [2^2 + 3^2 = 13]
3) Repeat the process until the number either EQUALS TO 1 or it loops endlessly and not reach 1, like this:

4) Numbers for which the process ends with 1 are HAPPY NUMBERS :)  and those that do not, are sad numbers :( [which means 23 is a HAPPY NUMBER!]

There are many happy numbers of course, with 1 being the smallest happy number, DUH. To simply see if a number you have thought of is happy, click here and use the happy number calculator to check!

We hope you are happier after reading this post. If you are thinking about changing your luck, why not read about lucky numbers here :)

Just Keep Swimming

On 13 August, 2016, last Saturday, our tiny nation won its first Olympic Gold Medal thanks to Joseph Schooling. He won the 100m butterfly stroke with a time of 50:39 seconds. Not only did he came in first, he also broke the Olympics record with this timing of his.

The competition also saw three swimmers finishing in runner-up position at the exact same timing, which got many people wondering - why do we keep seeing ties in swimming?

To help answer this, you can head to this website and read the article. The gist of it is that while we are able to construct a clock accurate enough to measure time to a high significant number, we are unable to do the same when constructing a swimming pool. Keeping the tolerance range of one pool's dimension to the next close to zero will make construction a nightmare. This is why we only consider the sport of swimming times down to a hundredth of a second, i.e. two decimal places, which results in the many ties we see in swimming competitions.

Perhaps when construction technology advances, pools can be made more accurately and we can then measure swimming times down to the thousandth of a second. Maybe, just maybe, there will be less ties.

Nevertheless, we want to applaud Joseph Schooling of his individual achievement in this year's Rio Olympics 2016. Thank you Jo! Keep the Singapore flag flying high!!

Fibonacci Sequence - What is it and how is it connected to the golden ratio

As promised, this blog post will be on the Fibonacci Sequence! (If you have yet to read the previous post on the Golden Ratio, do read it first before coming back to this post.)

Why did I post the rabbit photo in the previous post?

If you notice the number sequence on the right of the picture, it goes 1, 1, 2, 3, 5, ...which is actually the Fibonacci Sequence. What this means is that the reproduction cycle of living things, given that they reproduce in pairs, follows the Fibonacci Sequence! That's not all the Fibonacci-linked natural occurrences by the way...

Other Fibonacci-linked natural occurrences

Branching of trees

Spirals in a shell

Curves of a wave

And many many more...

So what exactly is the Fibonacci Sequence?
A sequence that satisfies the following equation is known as a Fibonacci Sequence.

So the sequence is as follows: 

F0 = 0

F1 = 1

F2 = F0 + F1 = 0 +1 = 1

F3 = F1 + F2 = 1 + 1 = 2

F4 = F2 + F3 = 1 + 2 = 3

F5 = F3 + F4 = 2 + 3 = 5

F6 = F4 + F5 = 3 + 5 = 8 

and so on...i.e. each successive number is obtained by adding the sum of the two previous numbers. Easy!

The Fibonacci Sequence Golden Ratio Connection

This is the fascinating part and why Math is fun! Remember the sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,... Dividing each number by the previous number gives 1/1 = 1, 2/1 = 2, 3/2 = 1.5, and so on, up to 144/89 = 1.6179. The resulting sequence will then be

1, 2, 1.5 1.6666.., 1.6, ...., 1.6179

You would realise that the numbers go up and down and keeps getting closer to you guessed it, the golden ratio, which is equals to 1.618. 

Because of this connection, mathematicians have actually found a connection that allows you to calculate any Fibonacci Number using the Golden Ratio. I'll let you brood over this equation and end the post here...

where Xn is the n th Fibonacci Number.

The Golden Ratio

Today, let's learn about the golden ratio. Phi, shown above, is the symbol that is used to represent the Golden Ratio. Phi is a constant, which means it represents a number, like Pi.

i.e. Golden Ratio = Phi = 1.61803....

How did this number come about?

The above shows how Phi comes about. Given an object of total length a + b, if it fulfills the above equation, then the golden ratio is fulfilled. To understand more about the equation above, refer to website and try out the "slider" function!

What is so fascinating about the Golden Ratio?
It has been known that if something follows the Golden Ratio, it somehow looks more beautiful and attractive. Let us be the judge of this by watching the following video:

After watching the video, decide for yourself if the person's face is more attractive because the golden ratio is fulfilled.

Golden Ratio in our surroundings
For the unobservant, the golden ratio is all around us as well. Here's an article on architects who have designed buildings around the golden ratio. Golden Ratio is especially prevalent in nature as well - read more about it here! If you have the time, head down to Lee Kong Chian Natural History museum for a closer look of the shells mentioned in the article.

People often link the Golden Ratio to the Fibonacci Sequence, so for the next post in our blog, look forward to learning more about the Fibonacci Sequence! For a sneak peek about the sequence, view the photo below :)

In Preparation of Haze 2016

The haze period of 2015 was in June - October. This year, to prepare ourselves for the haze (that hopefully will never comes), NEA has decided to phase out the 3-Hour PSI Reading in replacement of the 1-Hour PM2.5 Reading. The 1-Hour PM2.5 Reading will range from normal, elevated, high to very high or the Roman numericals I to IV.

A snippet of the poster created by NEA talking about the 1-Hour PM2.5 in more details. The full poster can be found here.

According to NEA, 1-Hour PM2.5 will provide a more accurate reading to indicate air quality compared to the 3-Hour PSI Reading. This will also put us in sync with the World Air Quality Index Project standards which uses the 1-Hour PM2.5 and not the 3-Hour PSI reading to measure air quality.

In addition, do note that when you refer to the air quality at haze.sg, there are several indicators reflected on the webpage such as 3-Hour PM2.5, 24-Hour PM2.5 etc. These readings are not as accurate as the 1-Hour PM2.5 reading as they may not be indicative of the current air quality conditions.

With this new update in NEA, we foresee that PSI may be phased out eventually in replacement of AQI, the standards used by the World Air Quality Index Project.

For now, let's wait and see and pray that there will not be a haze 2016.

Tau Day

Tau, known as the circle constant, is actually something you should be familiar with and here's why:

2 x Pi = Tau

and we all know what pi (=3.14159...) is.

So, if we were to recall the area of a circle in terms of tau and not pi, it will then be:

Area of circle = Tau x Radius

That means that the area of a unit circle i.e. Radius = 1 will simply be:

Area of unit circle = Tau

It seems that the definition of Tau helps to simplify mathematics, and so the boggling question is why are we using Pi and not Tau in most mathematics convention?

There are two groups of people in the Pi versus Tau game:

1) Here's an article on why Tau trumps Pi.

2) Here's an article on why Pi is the one way to go. (If this article is too lengthy, I would advise that you watch this video at least.)

Read them both and then decide for yourself if you prefer Pi or Tau. For those on the Tau-side, unfortunately, the mathematics world is still more keen on using Pi and so please stick to it.. For those on the Pi-side, please continue fighting for it as you never know when Tau might win over the hearts of the majority one day.

Before I veer off course for the focus of this blog post, today is Tau Day, the 28 of June, or more specifically 6/28 if you write the month first and then the day. This day has been designated as Tau Day as Tau = 2 x Pi = 6.283185.... (Yes, we mathematicians like to find all sorts of days to celebrate something mathematical.)

So, to celebrate Tau Day, please refer to here for all things Tau :) 

Have a Happy Tau-Tues-Day from us at the HSS Mathematics Department!

K E N D A M A

The link between math and physics is undeniable. Tadashi Tokieda is a Japanese mathematics professor specialising in this field. He is especially interested in toys and from his video explanation, we look at how mastering the art of Kendama can be made easier through knowing some basic math and physics!

P.S. I have tried the "tricks" out myself and they really do work.

In addition, there is an entire playlist of this particular professor's videos on Youtube that are intriguing and worth watching. Here's a link to it: Tadashi Tokieda on Numberphile. Some neat and simple mathematical tricks can be learnt from these videos. Do share it with your friends and see their faces grow in amazement!

The Story Of Calculating Machines

Calculating has been important for science, industry, and commerce from the earliest times to the present day. The word calculate is derived from the Latin calculus, or "little stone", referring to the ancient practice of using stones to perform calculations. Since then, more sophisticated devices have been invented to perform the complex calculations demanded by the advancement of science and technology.

Let's take a look at the revolution of calculating machines from 2700 BC all the way till today...

In 2700 BC:

The abacus is invented in Sumer (present-day Iraq) and is soon widespread. Till this day, abacus enrichment lessons are popular among children to help develop their mental sums. The abacus is a very simple tool to use as it can be easily understood from the image below.

In 100 BC:

The Antikythera Mechanism is an early Greek device used to calculate astronomical positions. It functions via a complex clockwork mechanism made of bronze gears. The device was first found at an archaeological dive trip 45 m deep in the waters near the Greek island of Antikythera which is how this device got its name.

In 1617:

This calculating machine, called Napier's Bones, was invented by John Napier. This set of inscribe rods or "bones" provides a quick way of multiplying or dividing large numbers. To learn more about how this machine works, read about it here.

In 1630:

Parts of a slide rule

English mathematician William Oughtred invented the slide rule to multiply, divide and even calculate roots and logarithms! It was the most popular calculating tool used by scientists and engineers before the advent of the pocket calculator.

In 1642:

The Pascaline was the first successful mechanical calculator. It was invented by Blaise Pascal. This calculating machine was capable of adding and subtracting two numbers directly and performing multiplications and divisions through repeated addition or subtraction.

In 1801:

The Jacquard loom was invented by Joseph Marie Jacquard. It is controlled by cards with punched holes, a system later adopted by early computers. It helped reduce the complexity of producing textiles with complex patterns. This machine was an important step in the advancements of computing world. More about its impact on the computing world can be read here.

In 1820:

Thomas de Colmar invented the Arithmometer. It was built as the first commercially successful mechanical calculating machine. Its sturdy design, accuracy and affordability made it reliable enough to be used daily in an office environment.

In 1822:

This majestic looking machine is known as the Babbage's Difference Engine, invented by Charles Babbage to overcome human error in compiling numerical tables. It uses the method of divided differences to tabulate polynomial functions.

Babbage's Difference Engine made out of Lego!

In 1889:

The electronic tabulating machine, known as Hollerith tabulator, was invented by Herman Hollerith in the USA and is the first device to use punched cards to store data rather than control a process.

In 1939:

The Bombe was based on a Polish design and was first built in Britain, by Alan Turing, during World War II to decipher codes produced by the Germans using the Enigma machine. If all of these sound familiar to you, it is because this machine was featured heavily in the movie - The Imitation Game.

In the 1960s:

Electronic desktop calculators emerged in the 1960s with the invention of the transistor. Pocket calculators like the one in the above image soon followed.

In the 1970s:

With the invention of microprocessor chips, it allowed for integrated circuits containing thousands of transistors to be commercially available for use in computers. This allowed for calculators in decrease in size and cost. By the end of the decade, calculator prices had reduced to a point where a basic calculator was affordable to most and common in schools and offices.

From 1980s - Present Day:

The microcomputer revolution took off in the 1980s as personal computers became smaller, more powerful and more affordable. The above image shows an early Apple computer. Computers are now becoming more and more powerful in processing information and churning useful and applicable results for researchers. It is an imperative tool in helping humans calculate at the speed of light and without us having to rack our brains much. Its usefulness is infinite if used correctly.

With technology improving day by day, year by year, who knows maybe down the road, another machine will takeover the computer as the one to rule them all... When that day comes, will you be the one who invented it?

Beauty Is In The Eye Of The Beholder

The above image illustrates how the Fibonacci sequence occurs in our natural surroundings. The Fibonacci sequence is one of the more commonly known mathematical sequences known to people outside of the mathematics field. It truly shows how Math is intricately sewn into our surroundings subconsciously and one wonders how beautiful that is! For more information about the Fibonacci sequence, please click here.

Next, beauty in Math can also come in the form of graphs. The above image shows the equation of the graph and the shape of its respective graph that will be formed. You can try the equations out if you have a graphic calculator with you. There are also plenty of other shapes and sizes of graphs you can form using a graphic calculator. There are even competitions for this which Henderson has competed in for the past two years! For more information about this competition, you can click here.

To sum up what mathematical beauty is, watch this video here and truly immerse yourself mathematically. As a prelude, do note that the video has been divided into three segments, the left segment shows the mathematical equation, the centre segment shows how the math related to the equation and the right segment shows its link to reality. Enjoy!

The Math Of Sports

Today, we look at how Math exists in sports. After reading the blog post, do find out more about how Math is integrated into other aspects of things e.g. Math in Science, Math in Nature, etc. You will then realise how Math is more integrated in our lives than we realise it...

Imagine that you have just spent a huge sum of your savings to book an airline ticket from Singapore to London just to fulfill your dream of watching your favourite football team play live. After flying for half a day and enduring a sleepness night on the plane, you finally reached your destination. 

You wake yourself up with a shower and then rushed to the stadium for the match of your life. When you arrived at your allocated seat, you realised that the person sitting directly in front of you is blocking you entire line of sight to the football field. You can't stand up because you will block the person behind. You can't move left or right throughout the game because that will distract the people sitting on the left and right of you. 

How could this have been prevented? Take a look here to find out how. 

When you are done, you can look here to see other ways in which Math is integrated into the sport of football. 

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Next, we talk about how Math is integrated into the sport of baseball. 

In sports, we want to win. As the coach of a team, we want OUR team to be the winning team. To give yourself a leg up in the game, you need to use statistics to understand your opponent better and then use it to your advantage. 

In baseball, a common statistics people look at is the batter's hitting percentage. This is calculated by taking the number of hits divide by the number of times batted. For example, if a player has a batter hitting percentage of 0.344 would mean that the player is able to get 1 hit out of every 3 times at bat. In the baseball world, that is a very good statistics and this player will be known as one of the strongest batter in his team. 

So if you are the coach of the team with this player, you would want this player to bat when bases are loaded. This will increase the probability of this player scoring more runs for your team, leading to a sweet victory.

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To be honest, there are many ways in which maths is integrated into sports. Do take the time to find out more on your own! We trust that you will do so :)

Square Root Day

As mathematicians and maths teachers, we like to always take the opportunity to celebrate any days or years that have the slightest link to maths. So here it is...

Happy Square Root Day Everyone!

Today, the 4/ 4/16, is square root day! Why? Because square root of 16 is 4! Can you guess what is the next square root day?

The next square root day will be 5/5/25, and that will be in 9 years time! If you have missed today's one, mark the next one on your 2025 calendar and celebrate it with your friends when the day comes :)

In order to decide whether a day is a square root day, you simply have to check if the date is in this format:

where x is a positive whole number.

To end it off, here are some ways you can celebrate the day ahead of you! Have fun!

Birthday Paradox

A paradox is a statement that contradicts itself, and yet might be true (or wrong) at the same time. So here we are, talking about the birthday paradox. If you want to understand this paradox better, we suggest you read up on your probability notes first.

Or is it happy birthday to a million people out there?

Imagine being told this - "Believe it or not, in a room with 23 people, there's a 50-50 chance of two people having the same birthday. In a room with 75 people, the chance of two people having the same birthday becomes 99.999%." 

Believe it or not?

Let's break down the problem here...

The first person can have any birthday. That gives him a 365 out of 365 possible birthdays, so the probability of the first person having the "right" birthday is 365/365 = 1.

Now, let's bring the second person into the picture. The chance of him having the same birthday as the first person is 1 out of 365. To find the probability of these two people having the same birthday, we multiply their separate probability = (365/365) * (1/365) = 1/365.

What about three people? The probability of the first and second person sharing the same birthday is still 1/365. The probability of the first and third person sharing the same birthday is 1/365 as well. What if the second and third person have the same birthday or all three people have the same birthday? Things are getting way too confusing now...

To solve this, we need to use a basic rule of probability which is the sum of the probability of the event occurring and probability of the event not occurring = 1. With this, let's start over again...

The probability of the second person not having the same birthday as the first is 364/365.

The probability of both the second and third person not having the same birthday is (365/365) * (364/365) * (363/365) = 0.9918.

The probability of four people having different birthdays will then be (365/365) * (364/365) * (363/365) * (362/365) = 0.9836.

If we keep calculating, we will see the number closing towards 0.5 as we reach 23 people, which means that there is a 50-50 chance of 2 out of 23 people having the same birthday. As we reach 75 people, the probability of 75 people having different birthdays will be close to 0 which means a 99.9% chance of 2 out of 75 people having the same birthday!

This graph gives you a rough idea of how the probability of two people having the same birthday increases exponentially as the number of people increase

So why is this a paradox? 

Let's read this article and understand it better. At the end of it, do try out the interactive example to convince yourself fully. Have fun!

Conclusion

The birthday paradox is actually a tautology i.e. true all the time. It is a paradox only because we are selfish humans (refer to article above).  The next time you have difficulty starting a conversation, why not share with someone about this paradox, it is a rather interesting topic to share about isn't it?

Pi Day

Today is March the 14 or 3/14 in the month/day format. This day is also celebrated by mathematicians as Pi Day, since 3, 1 and 4 are the first three significant figures of pi. As such, we are here to introduce some things you can do on Pi Day!

1) Eat a pie! (Or bake one and then eat it.)

2) Make a sky line out of the values of pi! (This is one of my favourites!)

Click here on how to do this.

3) Look for any digit in pi up to its 10 millionth digit here. Take note of any interesting properties you see about the value of pi and then go to the next point...

4) Recall the pi facts that you know or have learnt in school... Things like pi is approximately 22/7 or 3.14, pi is an irrational number, pi is the ratio of a circle's circumference to its diameter, etc. When you have exhausted everything you know about pi, then click here and explore the many more properties of pi you probably never knew about before today :)

5) Sprawl the internet for ridiculously pi-ish jokes like the one below...

(Hint for those who do not understand the above: Volume of cylinder = pi * r * r * h)

6) Sprawl the internet for insPIring mathematical quotes and motivate your friends with them.

7) Last but not least, go shopping for mathematics related items! Because you secretly know that there is more mathematics in your life than you want to admit.

Why Do We Learn Algebra?

In my opinion, there are two moments in the course of our education when kids fall of the math train... The first is when fractions are introduced. Until that moment, a number is a natural number - 0, 1, 2, 3, ... To go from this to the idea of a number can mean "what portion of" is a huge shift.

The next dangerous twist in the math train track is when algebra shows up. What we have been doing up till algebra showed up was to insert numbers into the addition box, or subtraction box, or multiplication box, or long-division box, and then report what comes out on the other side.

On the flipside, algebra is computation backward. For example, when you're asked to solve

x + 3 = 14

you know what came out of the addition box is 14 and you're asked to work backwards to find out what went in along with 3.

At this point, your teacher would have taught you that if you brought 3 over to the other side of the equation, things become like this:

x = 14 - 3

You will then put 14 and 3 into the subtraction box and find that x = 11.

Unfortunately (or not), it isn't always that easy. What if you need to solve a quadratic equation like

x^2 - x = 1

Apart from your teacher telling you to solve such equations, why would you ever bother? Well, let's think of a real-life application here. Imagine a missile flying furiously towards you. Maybe you know that the missile was launched 100 metres above ground level and has a upward velocity of 200 metres per second. Assuming that there are no gravitational forces acting on the missile, the height of the missile above ground level after x seconds can be represented by the following equation:

height = 100 + 200x

But, there is such thing as gravity. Which causes the missile to lose potential energy and arc back to earth towards you. The effect of gravity can be represented in the equation by adding a negative quadratic term, where it is negative because gravity pushes the missile down, not up. So the new height equation becomes:

height = 100 + 200x - 5x^2

As the missile is heading towards you, the most important question in your mind would probably be along the lines of am I save from the missile, where will it land? To find out this will just be to let height = 0, that is:

Find the value of x when 100 + 200x - 5x^2 = 0.

It is by no means that you know how to bring things to the "other side" to solve the equation. Maybe you don't need to. Trial and error is after all a powerful tool. If you let x = 10, the missile will be at a height of 1600 metres after 10 seconds. If you let x = 20, the missile will be at a height of 2100 metres, which means the missile is still rising. When x = 30, the missile is now at a height of 1600 metres again, which means that it has passed its peak. At x = 40, the missile is now 100 metres above the ground. And if you let x = 41, you get -105 metres, which means that the missile has contacted the ground between the 40th second and 41st second.

From this trial and error, you can see that as we carefully turn the time knob back and forth, we can get an approximate timing as to when the missile impacts the ground. However, is this solving the equation? It is after all still an approximate no matter how you fine tune your guesses.

Lo and behold, the quadratic formula is here to give you a satisfying exact solution. You may well have memorized this formula once in your life. But unless you have an unusually gifted memory, you probably won't remember it 10 years down the road. And this is just for quadratic equations.

What if we were asked to solve a cubic equation of the form x^3 + 2x^2 - 11x = 12. Fortunately, there is also a formula to solve cubic equations, but I won't bore you here for now.

The point is, working backwards is unconventional, and our human brains simply do not work well backwards. Algebra is tough because it requires us to work backwards. But it is a mathematical tool that is so strong that we cannot live without it. So where do we go from here...? We practice, and practice, and never stop practicing. The more problem solving questions involving algebra we expose ourselves to, the better we get. There will then come a time when we see that elusive unknown x and confidently tell ourselves that I will not be put down by this, I will find you x.

On what day of the week were you born?

Ever wondered what day of the week it was when you were born into this lovely planet we called Earth? Ever wondered what day of the week your 21st birthday will be so that you can plan the most awesome birthday party of the year? Ever simply wondered what day it is on let's say the 12th of March, in the year 4567 i.e. the date that will be read as 12-3-4567. Will you need to slowly count day by day from the year you are in now until the year 4567, or is there some short cut to all of this tedious looking and mundane calculations?

Now, let me share with you six easy steps to find out the day of the week of a particular date! We shall use 17 Jan 1942 as an example for our explanation.

Step 1: What is the date? 17

Step 2: What is the month? January. Then January is 6. Why?

A number is assigned to each of the twelve months. The assigned number is based on a formula which we will talk about later in the blog post. The table below shows what number is assigned to which month.

Step 3: We need to offset the decade? As the year is 1942, to offset will be 2. The decade offset from the year 1900 to 2010 can be found from the table below.

Step 4: What is the last digit of the year? 2.

Step 5: We need to offset leap years. For example, 1942 appears in an even decade (since 4 is even). The table below then tells us that the leap year offset for 1942 is 0 (look under the "2" column in the "even" row.)

Step 6: Add everything in red above from Step 1 to Step 5 will give you 27. Take 27 and divide it by 7 and find the remainder, which will then be 6.

6 = Saturday and you have your answer of which day of the week is this date!

To summarise, please refer to the following diagram:

(Source: Plus Maths - What Day Of The Week Were You Born?)

Sadly, the method above can only help you calculate until the year 2010 due to the restriction in Step 3. So how are we to find out the day of the week for dates after 2010?

Introducing the Zeller's congruence!

(Source: Wikipedia)

h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ...., 6 = Friday)

q is the day of the month

m is the month (3 = March, 4 = April, ..., 14 = February)

K is the year of the century (year mod 100)

J is the zero-based century 

Now, for those of you who understand everything about this formula may find out the day of the week easily using it.

On the other hand, there must be a lot of you who find that you do not understand the formula at all. Your brain is now going haywire from reading all of this unknown words and gibberish...Oh no!!

Fret not, as here comes the joys of internet. Simply click HERE and the website that you go to will help you find the day of the week within a split second! Now you can start planning for your future birthdays that fall on weekends and have the time of your life!

Sadly, the above formula and the website uses Zeller's congruence, which works only from years 1582 to 4902. If you try any year not in between the two years mentioned, the answer will NOT be accurate. That said, if you are as brilliant as Zeller, why not start a research in this area? Perhaps you will be the next person to come up with a formula that can calculate the day of the week for years before 1582 and after 4902!