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Geometry is being taught in the New Mexico United Locker Room! Thanks APS!

It’s APS Teacher Appreciation Night at Tonight’s New Mexico United Match!

By Professor Pitch| April 26, 2019 |

Tonight, it’s APS Teacher Appreciation Night at New Mexico United game. While I did not attend school in New Mexico, I do value my education and so therefore, I wanted to express my gratitude for the APS faculty for their time, efforts, sacrifice, compromise, and lastly their patience. You’ve taught student after student while running a household of your own.

I thought it would be cool to sit down and write a piece that had an education theme while, still being very relevant to soccer. I learned and I am sure you will find something interesting in this post as well. It may come as no surprise to some of you that soccer and geometry have some relation to each other. After all, soccer is a game of shapes, formations, and angles.


The pitch, which is the field, is a rectangular shape with other shapes creating boundaries, halves, penalty boxes, corner, and goals. So, the pitch is geometrically symmetrical. Setting up a wall at 10 yards or a goalkeeper coming off a line to reduce the target for a shoot, as Cody Mizell does often, has some impact on the cross, which is already a calculated trajectory. The cross has to bend in or out to give more advantage to the goal-scoring team. Bending it out allows for a more forward angle versus a completely perpendicular cross which is much tougher to head towards a desired target. The shot itself must take on a very calculated velocity, which encompasses angle and speed.


Team formation is not random. New Mexico United has been in a 4-5-1 or 4-4-2 formation through 8 matches so far. That formation count is broken down as defenders, midfielders, and then forwards. So, in this last game against Reno 1868, United had 4 defenders, 4 midfielders, and 2 forwards. This formation gives them more opportunity to score goals. In this game, midfielder Chris Wehan was position as a forward along with forward Kevin Frater. Forward Santi Moar was positioned as a midfielder. This puts a scoring threat on the second line as well. Let’s not forget about Josh Suggs, who is in a defender also referred to as fullback position. Suggs plays left fullback when he’s used as a scoring threat or he’s sitting as a center fullback when he’s used as a sweeper. The sweeper typically stays home to help out the goalkeeper. The 4-4-2 and 4-5-1 that United run with is at best a hybrid formation with scoring attacks in every line. This helps New Mexico score goals, play a stiff defense, maintain possession, or slow down the game tempo.


Connectedness: How many neighbor nodes does the person with the ball have? This is translated to how many passing options does the person with the ball have currently? If the formation remains in tact as it shifts up there are always passing options. New Mexico United maintains a 90 percent passing accuracy rating in its own half of the field.

Compactness: United’s formation must be like an accordion that can open and close, adapt and react, become dense and spread out. Compactness assists in defense and spreading out assists in offense. Its passing accuracy in the opponent’s half of the field is currently sitting at 67 percent. This tells you that formation shifts as it encounters opponents and therefore it must change fluidly throughout. United is resetting their formation once they are through the middle of the pitch.

Triangular formation in passing creates several opportunities for give-and-go. So, moving without the ball forms shapes that creates chances for the offense to score goals.

Lastly, let’s talk about the ball. Our featured image is as geometrical as they get and most resembles a soccer ball. I found this image online at Wikipedia and here’s the excerpt that accompanies it:

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal non-prismatic solids whose faces are two or more types of regular polygons.

It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.

It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces.

This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 (“buckyball”) molecule.

It is used in the cell-transitive hyperbolic space-filling tessellation, the bi-truncated order-5 dodecahedral honeycomb.


Featured Image Credit: CC BY-SA 3.0,

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