Agile & Waterfall, Unknown Twins: The Iron Triangle


This is the first of a series of 3 articles aimed to enlighten you about the art and science of Project Management and how it is deeply connected with logic, geometry, basic mathematics and common sense.

This series was born out of the discussions the two authors shared during the last three years about Project Management, Waterfall, Agile and other related topics. This series is also a consolidation of all the knowledge both authors accumulated during their past work experiences either working as engineers, directors or entrepreneurs.

Our simplified vision about Project Management, Agile and Waterfall will be published into 3 different articles, covering the following topics:

  • Part I – The Iron Triangle
  • Part II – The Paradigm Shift
  • Part III – The Art & Science Behind

Agile vs Waterfall

“Agile vs Waterfall…” The topic itself is such a strong and controversial one, that it is almost incomprehensible the huge amount of hours that both authors spent deeply discussing it. This was our starting point three years ago.

Assumptions are dangerous, as they can prevent us from getting deeper insights about a topic. When we discussed “Agile vs Waterfall” it was very easy to lose perspective and getting nowhere or have shallow, sometimes deceiving, conclusions. A waste of time and money as you know.

However, at the end of the process, we both concluded that the most fun, interesting, disruptive and surprisingly enlightening times that we have passed together, were the ones spent on digging our way through this journey by not taking any dogmas as granted and forcing ourselves to go deeper into Agile and Waterfall comprehension, until it made sense in our minds.

On the next 3 articles we will try our best to unveil what we believe is the truth that lies behind this “warfare” between “Agile and Waterfall”, why both models share the same roots and logic, and what their basic principles are.

We both learn a long while ago the power of asking the right questions. Nevertheless, this challenge forced us to re-discover this important soft skill once again by recognizing we were failing to do so and hence, wasting so much energy getting nowhere.

Suddenly, when we started asking the right questions, it was both liberating and revealing: the journey we are now sharing with you is our final outcome.

So let’s start with that.

What do “Agile & Waterfall” models have in common?

After a lot of discussion and study over concepts like scheduling, resources, scope, budget, risk management, critical path and so on, we have deduced the obvious: both models exist in order to manage projects, hence, they must and do share the same project management fundamentals and standards. It is just as simple as that, but not that simple to explain, as we will see throughout this series.

Only after arriving at this point (after almost one year after…) we really started this amazing journey on re-discovering the art and science of project management, sharing past and current experiences and taking down lots of notes on paper napkins.


Why “Agile & Waterfall” models are so different?

If same project management fundamentals and standards are shared by both models, why they seem so different? Are they really different? This one was hard: we started the discussion by digging into our past and current project management work experiences. And we were looking once again in the wrong direction. The answer was right in front of our eyes, the famous “Iron Triangle”:


The original “Iron Triangle” concept was invented by Dr. Martin Barnes in 1969 to demonstrate the connection between time, cost and output (correct scope at the correct quality). The correlation remains but the concept of the triangle is fading and becoming more complex. However, since most important software project management tools available on the market are based on this original concept (please check “Every Project plan is a triangle” written by Microsoft for its Project software product), we will center our line of thinking on this original basic form of the Project Management Triangle.

The “Iron Triangle” concept is so genius for being so simple: it’s pure mathematics and geometry in action as you will see. To start with, let’s recall the previous post “Delivering Value Fundamentals” and briefly explain what each edge of the triangle means.

On every project we have to manage 3 interrelated constraints. These are:

  • Time (T) – The planned amount of time available to complete the project;
  • Cost (C) – The budgeted amount of money available for the project;
  • Scope (S) – The unique product, service, or result to deliver;
  • Quality (Q), is not a constraint itself, it is rather the result of how well you will manage Time, Cost and Scope.

The Iron Triangle Geometry

As you already know, before you start a project you have to negotiate and sign-off all of the above 3 constraints with your client, either external or internal to your organization. What are you doing on these Initiation and Planning phases? If you excel on your job as a project manager, you are setting up a “perfect balanced” triangle, where Time, Cost and Scope have realistic and achievable values, and are in “equilibrium” with each other, i.e., all sides of the triangle are equal, hence an equilateral triangle. This is your ideal starting point.

Let’s dive for one second into the Ancient World: have you ever wondered why the Old Civilizations built so many artifact and architectural artworks using equilateral triangles as a foundation block? Some examples include some Egyptian pyramids, the Hindu Kali Yantra mystical diagram, old Chinese window lattices, the Greek Parthenon and the Pythagorean Tetraktys.

The answer is given by geometry itself: the equilateral triangle is a basic component of nature because of its perfect symmetry and simplicity and, as you may know, any image or shape can be expressed as a group of triangles, called triangulation. The equilateral triangle also shows up in many of the platonic solids that are the building blocks of complex three dimensional geometry. All crystal shapes for example can be derived from the platonic solids. In 3 words, the equilateral triangle is perfect, balanced and powerful at the same time.

And how about Quality? Well, as you can imagine, Quality corresponds to something within the starting equilateral triangle. What exactly? The triangle’s area? The answer is not so obvious. And why not search for some answers once again in the Ancient World?

What is the oldest form of geometry known to men? The answer is the circle: natural circles have been observed since the beginning of recorded History (remember the Moon?). And from a mathematical point of view, the circle was also the starting point for the development of today’s Geometry, Astronomy and Calculus sciences. The wheel is the final perfect example.

And why not the Area? Simple again: imagine you can have 2 triangles sharing the same area, one a perfect, balanced equilateral and another a distorted scalene. If Quality would be represented by the area, how do you differentiate it between these 2 triangles sharing the same area? The answer is: you can’t. And because you can’t, you are implicitly admitting that Quality is also a balanced measure of your project:


As we can see above just by using inscribed circles, you can have 2 different triangles sharing the same areas, but less Quality on the “unbalanced” one: the more unbalanced the triangle is, the less Quality you will end up having at your project closing. Pure geometry.

For you to clearly understand this concept, let’s start from the beginning: you have initiated your project with a predefined Time, Cost and Scope negotiated with your client and with an implicit maximum project quality to achieve. Now imagine that you finish your project after a few weeks, months or years with different Time, Cost and Scope than the original ones (which is the reality of most projects). Your goal is to end your project as closer as you can from the starting equilateral triangle. Potentially you will end up with a scalene triangle, with deviations from the original signed-off Time, Cost, Scope and hence, Quality.

Finally, what does geometry mean? In management lingo, two things:

  • Time, Cost and Scope are the 3 sides of the “Iron Triangle”, therefore they are indeed interrelated: you can’t change the length of one side of the triangle without modifying at least one of the other two. In other words, you can’t change your project’s budget (cost), schedule (time) or features/requirements (scope) without affecting at least one of the other two constraints.
  • Quality is deeply related with the 3 constraints, since Quality is the inscribed circle: if you modify one of the 3 project constraints during the course of your project you are indeed changing the expected project Quality.

The Iron Triangle Mathematics

Now let’s use mathematics, namely linear equations with three variables, to see the triangle perimeter revealing itself. Generally speaking, a triangle perimeter is given by:

Side A + Side B + Side C = Perimeter


When you finish the Initiation and Planning phases with your client, besides negotiating the project Time, Cost and Scope of the “ideal” equilateral triangle (the starting triangle of your project), you are also predefining a perimeter value for the triangle as you did with the inscribed circle (Quality).

It’s relatively easy to infer that, in order to preserve the original equilateral relationship between Time, Cost and Scope during the entire project lifetime (always remember the inscribed circle), you will try to do your best to maintain this original perimeter value. Therefore, we can then see this initial perimeter as a constant fixed value K that will guide you, through the perimeter formula, on managing your project life cycle:

Time (T) + Cost (C) + Scope (S) = Constant (K)

The above is a linear equation with 3 variables. And, if you recall your high school math studies, you can only solve this mathematical problem if you have 2 more linear equations with the same variables, the so called “systems of linear equations”.

But, in the real world of project management, you don’t have systems of linear equations. As said in the beginning (and we will go deeper on Part III of this series), Project Management is both an art and a science, not a simple mathematical problem to solve.

By summing up the above formula with the equilateral triangle, we re-validate the following sentence widely accepted by the Project Management community:

You can’t change a project’s budget (cost), schedule (time) or features/requirements (scope) without affecting at least one of the other two parts.

If you try to answer the following questions using the perimeter formula, you will get the full picture:

  • If you decrease T (the amount of time available for you to complete your project is reduced for whatever reason), how will the other variables behave? Do they all go up (both C and S), or just one goes (C or S)?
  • If you decrease C (just imagine your budget had major cut in the middle of your planned schedule), how do you adjust your project to maintain K? Do they all go up (T and S), or just one goes (S or T)?
  • Your questions, your scenarios, just question yourself…

We could go on, and on with this… And the truth is, you can’t answer the above questions in a simple manner.

Understanding the Constant K

How do we solve the above linear equation with 3 variables perimeter formula without any other help (other equations, other formulas, etc…)?

The answer is: we will simplify the perimeter formula, downgrading the 3 variables linear equation to a 2 or 1 linear equation.

Let’s start with a simple example:

Imagine that the Scope is predefined by your client at the beginning of the project, meaning, no matter what you do, you will have to deliver the features/requirements outlined in the original stakeholders specifications. This is the case of a house, a bridge, a rocket, a car, a book, a movie, a song, etc…

So, if we are fixing upfront the Scope (meaning, it will remain the same till the end of your project), we can add it to the fixed Constant (K) part of the above perimeter equation, simplifying the formula to:

Time (T) + Cost (C) = Constant incorporating Scope (Ks)

What does the above formula tell us? Simple: you only have to manage Time and Cost. In other words, these are your only 2 estimated variables that you will have to manage.

Now, let’s answer some management questions based on the simplified formula:

  • If you decrease T (Time), how will C (Cost) behave in order for K<sub>s</sub> to remain constant? The answer is obvious: it must go up. In other words, if your project schedule has been cut you will have to throw money into your resources’ pool (people’s skills, equipments, etc…) in order to meet the new deadline.
  • If you decrease C (Cost), how will T (Time) behave in order for K<sub>s</sub> to remain constant? You already know the answer: T must go up. In other words, if your project have suffered a major cut you will have less resources to allocate and, therefore, your schedule must be extended.
  • Your questions, your scenarios, just question yourself again and again…

The given example (fixing Scope) was one among several examples that could be used. As you can imagine, there are a few approaches to solve the 3 variables perimeter formula. This is where the Project Management Models and Frameworks come into play. Two of them are Agile and Waterfall. But always remember: the above mathematical perimeter formula is the common base foundation for all different project management approaches we will talk about on the next articles.


So, have we fully answered “Why Agile & Waterfall models are so different?”?

NO, not yet, we only have given you the concepts needed to answer it properly. Only on next articles of this series we will try to do so.

Stay tuned for the next post:

“Agile & Waterfall, Unknown Twins: The Paradigm shift”.

To Be Continued…