Role of Geometry in Management Science

My daughter is very animated when she speaks - shaking her hands vigorously,her face expressive, however the moment I hold her hands together she turns silent. Similarly I think the training consultants would be lost for words without the geometrical shapes they use to explain concepts. Long ago, as a young engineer attending training classes, I was bombarded with triangles, quadrants, circles and many other shapes by the trainer in his presentation. I felt he was using these to show-off his knowledge and impress young impressionable minds. Now, after many years of being part of the management, I truly appreciate the clarity these geometrical shapes bring to any organisational training presentation. I decided to explore the different shapes used in management science in todays blog.

Most of the content of this blog is courtesy "Google Images Search Engine". I searched for shapes in leadership and management. For example I typed "Triangle in Leadership" and it displayed many images. I picked a few to make my point. So this blog will have more pictures than words (After all a picture is worth 1000 words ,so you actually get a good deal :-)). This will also keep happy my friend and colleague who suggested that I add more pictures to the blog.

To build a structure to this blog, pause for a moment to think if some management concept can be explained by way of a line. Except for the Top-Line and the Bottom-Line that the management is concerned about, you would not find many uses of the geometrical figure "line" in any presentation. Unless, of course, it is a graph showing whether the manager took actions or not as given in the below picture:



The typical shape using two lines usually takes the form of an x-y axis. This creates four quadrants. Quadrants have been used extensively in management science. A popular example, of the usage of the quadrant, can be found in the book "7 habits of highly effective people" by Steven Covey as shown below:



This quadrant usage has become so popular, that people talk about doing more of 2Q activities when refering to doing important but not urgent tasks. Similarly we are advised to do effective time management to move Q3 activities to Q2. It would be difficult to appreciate these concepts without the use of quadrants.

Yet another example of the usage of quadrants is the situational leadership style.



One of the critical tools used for organisational development is the Performance Potential Matrix which is a 3 X 3 matrix. It is used for managing human capital and is an efficient way to find out who and where your high potentials and high performers are - A very good succession planning tool. Aim to get boxed into #9 box which is at the top right corner.



With three lines, we get the most used geometric shape in the management science - the Triangle. Any time you have three parameters and you want to emphasise the relationship between them, make a triangle and make each of the parameters a vertex. Below is an example of the leadership model. By having Strategic Vision, People and Communication as the three vertices, the author emphasises the relationship between these parameters. He very nicely maps the What,Why and How to these parameters and puts the "YOU" in the center.



But the most famous triangle model is seen in Project Management, to explain the tradeoff between Scope, Cost and Time:



The other famous shape used in the management science is the pyramid. The maslows hierarchy of needs is best described in the form of a pyramid. The basic physiological needs forms the base of the pyramid with the self esteem needs placed at the top of the pyramid.



Another self-explanatory example of the leadership pyramid is shown below



Circles too have a place in management science. Again, the most popular usage of circle comes from Steven Covey's book on "7 habits of highly effective people". "Habit 1: Be Proactive" is particularly useful when you feel powerless against life's forces. Covey recommends that you examine what you can do, instead of focusing on worries over which you have no real control. First notice all your concerns. Among those concerns, determine where you can take action.Think of ways to be more proactive (not aggressive) and address the things you can do something about. Your circle of influence will enlarge and your circle of concern shrink.Covey distinguishes between the have's ("If only I had...") and the be's ("I can be..."). Focusing on what you don't like is disempowering. Focusing on what you can do is proactive and empowering. "Be part of the solution," Covey suggests, "not part of the problem." Circles convey this profound concept very lucidly.



The Circlular shape is very effective when required to communicate many parameters or offerings. Like the wealth management solutions described below



Talking of circles, we cannot forget the Venn Diagrams. I could not find many examples on the Venn diagram being used in management science, but found one that is creative. It may be a good exercise for the readers to find out where they belong to in this venn diagram. Without doubt I can see Sachin Tendulkar in the "Hooray" region.



I was wondering if I would find some example for hexagon. To my surprise I hit upon Holland's hexagon.Dr. John Holland is a highly respected vocational psychologist who developed a popular system to help individuals identify vocational theme areas that best suit their unique personal profile.In the Holland framework, there are six vocational themes : Realistic, Social, Investigative, Enterprising, Artistic and Conventional. These themes can be arranged in a hexagon as presented below. The themes that are closest to each other are most similar; the themes that are opposite one another are the most different from one another. You may also identify with a second or possible third theme. Your combination of career interests can help you to understand what types of work and learning you would enjoy and do well.



Journal of Career and Technical Education had a research paper that constructed a visual model to provide greater understanding of the competencies and traits required of successful agricultural science teachers. Given that seven categories were identified (Instruction; Student Organization; Supervised Experience; Program Planning and Management; School and Community Relations; Personal Traits; and Professionalism), a heptagon was chosen for the general shape of the model (see below). The newly identified competency, “working with diverse groups” was deemed by the research team to transcend and interact with all seven categories. Thus, this competency was placed in the center of the heptagon with double arrows extending to each category.



Can you imagine a model which is a nonagon ? Tough isn't it ? But a very ancient tool for understanding ourselves and others is called ENNEAGRAM and it describes nine different personality types or ways of seeing the world. It helps us understand how each type has certain ways of filtering information so that attention returns in habitual ways to repeating patterns. By revealing these largely unconscious patterns that drive our personalities, the Enneagram provides a key for unlocking our capacity for greater choice, freedom, self-awareness and compassion.



If I continue searching,perhaps I would find models that use geometric shapes having ten or more sides.I guess I have made my point, with various examples, that geometry plays an important role in the science of management.

Happy Reading

-Ram