The role of geometry in castle engineering and architecture


The medieval builders were masters of geometry in their time. Many of them had access to ancient books and texts that contained teaching materials for ultimate castle shapes. The role of geometry in architecture has many layers. This branch of mathematics provides aesthetic and functional design benefits. The study of architecture geometry was not customary at your average 14th-century college, therefore, highly educated builders were valuable assets.

In this article, we are going to examine the role of geometric shapes in architecture. We will analyze the influence of different geometric shapes on defensive capabilities and aesthetic appeal. And also, how the use of mathematics in the building construction process provides economic benefits.

The circle as the optimal shape

At any level of education, math represents a bitter pill for most students. This goes for geometry too as one of its branches. Many students these days have difficulties understanding both geometry questions and answers, alike. Many online portals provide answers to high school geometry questions, and a website called Plainmath is one of these platforms. However, for medieval builders, missing out on a lesson was not an option. They had to soak up as much knowledge and even go through texts that were forbidden at the time. After all, their work could save thousands of lives or leave the inhabitants at the mercy of their invaders. 

To protect a castle, engineers needed to build strong walls. However, strength is not always decided by the type of material we are going to use. The shape of the castle walls plays a significant role in their defensive capabilities. A circular design was the most popular medieval wall design for several reasons. First of all, the circle provides the best surface to defense perimeter ratio. This means that you can fit the most people inside and have the smallest area to defend. 

Next, there are no blind spots inside the circle, so the soldiers can always see each other. Another notable aspect of the circular area is the absence of weak spots. When you have a perfectly round wall around you, every point is equally challenging for the invaders to breach. Shapes that lack symmetry have points that are weaker and the enemy would concentrate their fire on one of those points. The defenders would have to move to the endangered part of their defenses and leave another part of the wall without proper manpower.

Combining different shapes for ultimate efficiency

The use of circular shapes in castle architecture has numerous advantages, however, it’s not easy to build a perfectly round building. Medieval builders had to be efficient in many ways. They had to come up with a method to build a resistive castle in the shortest timeframe. The amount of materials that are going to be used is also an important aspect to keep in mind. Most importantly, the building should provide space and security for a large number of people in case of an attack. 

It was much easier to build rectangle-shaped castles than round ones. However, the rectangular shape had many disadvantages that should be neutralized. Each great builder went through their respective school of engineering, so there were naturally diverse approaches to this issue. The most common architecture geometry principle included the combination of square and circular shapes. 

Improving the line of fire

When it comes to defending your walls, the line of fire plays a vital role. The archers and other ranged units needed to cover every approachable point. With rectangular walls, this was all but impossible. When there’s a straight wall in front of a ranged unit, there’s always a blind spot that the arrows can’t reach. However, placing a circular turret on each corner of the wall extends the reach of projectiles. For this reason, we have dozens of medieval castles with round turrets on the corners and often above the main castle gate.

Increasing defensive capabilities

Apart from blind spots, castle builders five centuries ago had to ensure optimal range for defensive units. One of the most interesting methods of increasing defensive capabilities was to build a hexagonal wall with round turrets on each corner. This gave the defenders a clear line of sight and the ability to cover a wide area. They could even aid their comrades on the neighboring turrets if needed.

Other notable methods of the use of geometry in castle engineering

Symmetry is a geometry form that’s widely used in medieval castle engineering. The builders used symmetric forms to ensure the aesthetic appeal of their buildings. Furthermore, these types of shapes make a sturdy construction, so they had a practical role, too. 

The star-shaped walls were used to detain attackers through offense rather than defensive maneuvers. It allows flanking fire against those invaders that are hiding at the base of the castle wall or trying to use siege ladders. As we mentioned earlier, the builders had access to ancient texts which gave them knowledge of Pi and the Golden ratio. These two allowed engineers to design aesthetically appealing castles that would endure through time.


Geometry has been the building block (no pun intended) of engineering since the first structures were raised. From the Great Pyramids of Giza to Gaudi’s Sagrada Familia geometric shapes and principles were at the base of monumental buildings that witnessed the centuries. What’s amazing is that medieval builders had to struggle to obtain knowledge, as most books were forbidden during the middle ages. However, geometry is all around us in nature’s design. So even if we draw inspiration from nature alone, we can learn about geometry. And so could the engineers of the medieval period. 

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