Category: Summer Camps & Post Primary Education

Summer Camps & Post Primary Education

Madigan gets the nod…Leinster to Win

Should the game come down to conversions of tries, as we believe it will,  it’ll be the kicker who picks the optimal place to convert the try.

ian madigan

So how should a player (without a measuring tape or protractor) choose which place to kick a conversion from? He can choose from anywhere along the red dotted line as shown here (having scored a try at the goal line where the red dotted line begins):

red conversion line

Firstly, it can be seen that maximising the Hughes Angle H (named after the man who first tackled (!) this problem) will help:

hughes angle

Maximising this angle H will increase the margin for error and increase the chances of the ball going between the posts (we’ll deal with the height and angle of the kick in a second):

With a bit of Pythagoras and some other useful mathematical techniques (details of which are available in another post to go up this weekend for those interested), it can be shown that kicking from where the circles touch the conversion line (in other words, where the conversion line is a tangent to the circle) will maximise this angle:


circles edited

It can then be shown, that the optimal kicking lines are:

optimal kicking points


Now, given that the ball has to travel over the bar, we can add this constraint to the maths. When a kicker kicks the ball, the ball will follow some line which can be traced by of a cone shape of some sort and we have a new angle R, the raised Hughes angle to consider:

conical angle and elevation angle


There is a point where E, the angle of elevation of the kick, is minimised while still permitting a successful kick: this is the point from where the flattest feasible kick will be flying horizontally as it clears the crossbar. We then, as always, have a trade off , between wanting both to minimise E and to maximise H. The precise point where the raised angle R is maximised will be somewhere in between.

The long and the short of it means that for example, kicking with an elevation of E = 35 degrees, the effective angle is 18% smaller than the Hughes angle. By comparison, kicking with an elevation E = 20 degrees, the effective angle is only 6% smaller.

rugby ball and posts

As Hughes himself puts it: “The moral is, all else being equal, and as long as the goals can comfortably be reached, the player should kick at as shallow an angle as possible.” So the kicker will need to try and minimise the angle of elevation of the flight of the ball (E) while also maximising ‘Hughes Angle’.

God Help the kicker when he starts placing the ball, because if he gets this right, the rest will surely follow.

So, familiarity with the pitch, its dimensions and scale will be a factor for the kickers on Saturday, now that Ian Madigan got the nod coupled with his academic background, Leinster will outmuscle Munster on the mathematics  front and win by a conversion!


Summer Camps & Post Primary Education

Mathematics – The Philosophy of Educated Risk Takers

“Education should embrace more than formal learning”,

John Lawlor, Chief Executive Office, Scouting Ireland, Irish Times, March 25th 2014.

We agree wholeheartedly with Mr Lawlor’s assertions presented in the Irish Times yesterday that the changes proposed in the Junior Cycle afford great opportunities to students to enrich their post primary experiences and to achieve a balance between formal and informal learning.



Surf 3D Right Side Up







We would go a step further and say that it is an essential part of a complete education where students will have greater freedom in acquiring essential life skills as well as coming to terms with the underlying philosophy that underpins all learning and personal development, whether in or outside of the classroom, embracing critical thinking, educated risk taking, collaborative thinking, problem solving, decisions making, appreciating change and rate of change in all things and aspects of life and relationships. This philosophy is of course Mathematics. This is the one true philosophy that not only underpins all subjects and disciplines but also holds the key to successful, caring and progressive societies.

Complimentary Customised iBooks are given to students who also have access to iPads as part of the technology based learning environment.
Discovery, Creativity & Technology embracing educated risk taking at CMA

‘Máthēma’, the ancient Greek word means ‘that which one learns’ and in modern Greek simply means ‘lesson’. There have been many other definitions since then such as Aristotle’s definition ‘the science of quantity’ up to as late as 1870 with Benjamin Peirce’s  ‘the science that draws necessary conclusions’. Whichever definition one prefers, mathematics can be seen as a fundamental philosophy whereby people can understand the world around them enabling them to aspire to be masters of their own destiny, whether it be through a university degree they would ideally like to complete or a career they would love to follow or a business idea they have and need to be equipped to pursue.

When students have been afforded the opportunity to grasp the key concepts through more informal strategies, and are comfortable with them, their career choices are increased many fold, leading to happier and more satisfied citizens. Regardless of whether a student has an academic career path in his/her sights or perhaps a career in a trade or business, having a fluency in the key mathematical concepts will go a long way to achieving these goals while ensuring a sound mind capable of educated risk taking and participating in a caring and more equal society.

In conclusion, John Lawlor’s assertions are indeed correct, and with clever and astute school led curriculum design, the new Junior Cycle offers amazing opportunities for students to discover and develop their interests, to bring rational and critical thinking to their daily lives while embracing the wonders that creativity and mathematics can foster.

Aengus O’Connor, Director




man utd

“You’ll never walk alone”

Bill O’Herlihy and RTE can take solace from the fact that they are not alone. From the OECD (PIAAC) study in 2012, just over 25% of Irish adults score at or below Level 1 for numeracy compared to a 20% average across participating countries.

While Bill’s contribution to the debate was hilarious, there is a very serious and expensive underlying issue behind all of this.

In the UK, in a study published on 11th March last week, a team of Pro Bono Economics researchers produced analysis that puts as its central, conservative estimate, the cost to the UK of poor adult numeracy at £20.2 billion per year (or about 1.3% of GDP).

We really need to encourage our children to become fluent in maths, just as we do with languages such as Irish, French and any other we choose. Total immersion and creative connections with real experiences are the key components to such fluency.

Can Ireland’s woes be largely down to many of our business leaders and politicians having a really poor fluency in mathematics? Imagine a Bill O’Herlihy type gaffe at a Central Bank Of Ireland regulation meeting with Bertie and you get the idea.

Fluency in maths is attainable and could save the country a fortune while dragging it out of the mess we’re now in.

Summer Camps & Post Primary Education

Why is the sky blue?

Why is the sky blue?
Cashel, Connemara, 2014


For many a year scientists and poets alike pondered on why the sky was blue. Many thought that it was due to small droplets of water vapour in the atmosphere and indeed many still do. If the droplets of water vapour did indeed cause the blue colour we see, there would be more variation of sky colour depending on the variation of humidity, and this isn’t the case. A cloudless sky is as blue in Saudi Arabia as it is in Connemara.

So what does cause it?

We can thank County Carlow and one of its resident scientists John Tyndall for the answer to this question.

John Tyndall discovered why the sky is blue.
John Tyndall discovered why the sky is blue.

Tyndall discovered that when light passes through a clear fluid which has small particles suspended in it, the blue light scatters more strongly than red light. This can be easily shown with a tank of water and a little soap; when a beam of white light flows through the tank from one end to the other, at the sides the beam of light can be seen through a blue light while the light seen directly from the end is reddened.

The Tyndall Effect can be seen in this piece of opalescent glass where the orange light shines through while the blue light gets scattered within the glass.

Tyndall Effect
Tyndall Effect


So the next time you look up at the sky while the sun shines white light at the earth, its the blue light being scattered by the molecules in the sky that is giving the sky its blue colour while the red and orange colours shine through to us on the ground, giving the sun its yellow/red/orange hue.