10 Times the Golden Ratio Was Used in War

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Many enmeshed within the world of art are well aware of Pythagoras’ discovery of the Golden Ratio – a mysterious figure that is inherently beautiful. Just what is that ratio? 0.618, or around 3/5. Anytime you have a painting that utilizes this ratio, it will be recognized to have traits of beauty within it. Photographers will recognize the ‘rule of thirds’ present within the Golden Ratio, being a rough estimate of 0.618.

Of course, the painter’s skill with a brush, the subject matter, and the time spent on the final piece are also vital components of determining how beautiful a piece will be, but the point remains: there is something inherently special about the Golden Ratio.

But are there other aspects of life where we can see the Golden Ratio at work? Can it be applied to fields other than art? What about the field of war? History appears to instruct us so. If we examine the life of war throughout history, we can find multiple examples of the Golden Ratio being applied successfully, resulting in victory for the man who uses its secrets, knowingly or not.

And while generals throughout history may not have realized this was what they were doing – using the Golden Ratio – the fact remains that it still seems to benefit the user. Perhaps mathematical beauty applied to war is an ingredient for constant success? Perhaps it can warn us as to when conflict is soon to turn sour?

If we take a closer look, I think you’ll be surprised at what we find out…

10.) The Battle of Arbela 

War is part art, and few displayed this as well as the man who would have “The Great” tacked on to the end of his name: Alexander.

Alexander the Great would demonstrate his ability to paint a masterpiece with his sword at the Battle of Arbela, where he would finally vanquish his long-time foe, King Darius. The two men had fought each other for years, with Alexander even going so far as to capture Darius’ family.

The Battle of Arbela was identified by both men as to be the final decision as to who would reign throughout their section of the world. Both men were formidable enemies to behold, and knowing he was in for no easy fight, in preparation for Alexander’s attack, Darius set about fortifying his position as best he could. Obstacles and traps were placed throughout the battlefield, scythed chariots were pre-positioned so that they could best mow down enemy troops, and longer swords and spears were handed out to his men. By some estimates, Darius’ position was a million men strong.

He should’ve been unstoppable.

Yet Alexander was able to take the field and become King over all Asia with only 40,000 men.

How did he do such? Aside from ensuring his men were well-rested, learning of the positions of the traps from POWs, and keeping his men well-fed, Alexander also seemed to have a little golden help.

As the battle began, Alexander sent much of his right front towards Darius’ left flank. As the men approached one another, the Macedonians then turned to hit the “golden point” of Darius’ front line – hitting approximately 3:5 of the way down Darius’ line.

Darius’ troops were separated, Alexander took the field, and the rest is history.

9.) The Characteristics of the Mongolian Hordes

None could strike fear into the heart of Medieval men as could the Mongols. Traveling light and seemingly as fast as light itself, these mounted soldiers seemed to be an unbeatable foe. And at the head of these Mongol hordes was a man simply known as the “Universal Ruler” – Genghis Khan.

Throughout his lifespan, Genghis Khan would go on to conquer the largest landmass of any human being in history, taking over somewhere between 11-12 million square miles of land, roughly the size of Africa.  This massive landmass would eventually result in being a large part of the reason the Mongolian empire crumbled – it was too much land for too few men – but the feat alone was an act of military brilliance.

Using horse-mounted dummies to trick his enemies into thinking his army was stronger than it truly was, being experts with archery on horseback, and the ability to move with minimal equipment were all some of the reasons that the Mongols were able to conquer as much landmass as they did, but could the Golden Ratio apply here as well?

It appears so.

The Mongols had a very different cavalry formation than did the rest of Europe. How so? The Mongols had an approximate 3:5 ratio of heavy to light cavalry. For every four heavy cavalry soldiers, the Mongols had six light cavalries. This combination seemed to be the perfect mix for dealing with European defenders as the heavy cavalry could sweep through the aftermath the light cavalry had picked off from a distance, once more showcasing the role of the Golden Ratio during war.

8.) King Gustavus of Sweden 

Perhaps no other medieval warrior applied the Golden Ratio as effectively as did the man who could go on to be known as “The Lion of the North.” Taking the throne at the age of 17, King Gustavus had no easy transition period. At his coronation, Sweden was in the midst of a war with Russia, Poland, and Denmark, all whetting their swords for Swedish blood.

At the time, battle had largely grown into a logistical nightmare. European countries largely had similar weaponry, and generals had turned to using wars of attrition and outmaneuvering one’s opponent to bring about surrender.

The only problem with this was the cost of resources. To move an army is expensive, and to engage in attrition warfare even more so – in cost of ammunition, food, weaponry, and lives. Knowing that Sweden would never be able to survive such warfare economically intact if he used these methods, Gustavus instead focused on changing his tactics.

He took his brigades – composed of three 500-men squadrons – and made 2/3 of each of them musket men as the remaining third remained pikemen.

The resulting combination led to a devastating combination of weaponry, revolutionized the role of firearms in warfare, and helped to propel Sweden to being a powerful force to be reckoned with throughout Europe at the time.

All because a 17-year-old kid was willing to think outside of the box. Perhaps he had studied Pythagoras?

7.) The Battle of Trenton

The element of surprise certainly matters. And when it’s compared with the Golden Ratio? Well, then you may just have a recipe for the complete annihilation of your enemy. On Christmas night, 1776, George Washington rallies his men for a raid across the Delaware River.

Their target? The German mercenaries, known as Hessians, who reside ten miles away at the town of Trenton. Washington concocts a three-pronged attack, but bad weather forces two of the columns to have to turn back. A third of his men make it through, however, and Washington is able to catch the invaders completely unaware.

It appears that Washington’s three-tiered attack ended up being a three-layered insurance policy.

A total of 2400 men join Washington for the fight against a force of 1500 unexpecting Hessians. This means that out of the 3900 men engaged in the Battle for Trenton, Washinton held roughly 61% of them, a perfect match with the Golden Ratio.

And it most certainly didn’t fail him either. By the end of the battle, there would be 905 Hessian casualties and POWs, while only five casualties remained on the American side. This means that roughly 60% – another close match of the Golden Ratio – of the Hessians were defeated at Trenton.

Is this coincidence? Or perhaps, is it something more? We’ll leave that up to you to decide for yourself.

6.) The Battle of Yorktown

Even within the American War of Independence, we can find evidence of the Golden Ratio at work. George Washington was not only an architect of human freedom, but it appears he was something of an artist as well.

After hearing that a French fleet was going to be available to lay siege south of New Jersey, Washington and Rochambeau marched their 8000 Continentals to meet up with 12,000 militiamen, French, and Continental soldiers – a wonderful 2/3 ratio.

As the siege of Yorktown began, Washington’s men blasted away at the British fortress with their artillery. Over 15,000 artillery rounds would be fired by America into British defenses, and the abundance and accuracy of the fire were so pronounced it had a massive impact on the British desire to surrender.

But did the Golden Ratio play out even with the choice of artillery used?

It appears so.

At Washington’s command were three 24-pound cannons, three 18-pound cannons, two howitzers, and six mortars. With 58% of Washinton’s choice of artillery being cannon, it appears we become dangerously close to the 0.618 of the Golden Ratio.

Perhaps a fuzzier correlation, but as military theorists have pointed out, the Golden Ratio often results in fuzzy applications.

5.) The Golden Ratio Protects Russia from Napoleon

Even in the cautionary tale of Napoleon’s invasion of Russia, we can find the Golden Ratio at work. In June 1812, Napoleon made the fateful decision that historians would argue about ever since: he invaded Russia with 500,000 men.

While he was initially largely successful – winning the Battle of Borodino – and largely having the Russians retreat into the interior in front of him, it was once he entered Moscow in September that things began to take a turn for the worse.

Terrible roads made resupply difficult, the Russians’ scorched earth policy and poor planning left the French woefully unprepared for the bitter Russian winter that was to come. By October, Napoleon realized that to spend the winter in the city was an act of suicide, and a retreat was sounded.

Three months of victory had been followed by two months of retreat (a 2:3 ratio) as Napoleon’s men attempted to make it back to warmth and safety.

Napoleon lost 300,000 men – 60% of his forces – and the end result was his being exiled to the island of Elba.

4.) The Battle of Harper’s Ferry

Divide and conquer? It does appear there are sometimes such a position can indeed work, and one need look no further than the Battle of Harper’s Ferry for evidence of such.

The Union Army has taken the town of Harpers Ferry, threatening Robert E. Lee’s chances at communicating with Virginia or receiving any resupply. At the moment, Lee and his men are in Frederick, Maryland, and if they want to have any hope of not starving to death whatsoever, Harpers Ferry must be taken.

However, Lee must weigh the balance of determining how many of his men he can safely dispatch to Harpers Ferry without leaving the remaining men in Maryland exposed to Union forces.

He settles on sending 2/3 of his men along with Stonewall Jackson to deal with the threat.

Jackson is able to outflank the Union men with artillery from a nearby mountain, Harpers Ferry is won by the South, and Lee’s men are able to stay alive long enough to plan their next course of action. What’s interesting, though, is that the Union commander at Harpers Ferry had come into contact with a lost copy of Lee’s battle orders for the day, communicating such to his superiors.

Had it been revealed that Lee’s position was woefully undermanned, this could have easily spurred on an overwhelming counterattack by the North against Lee’s men in Maryland.

However, the Golden Ratio seems to have served Lee well here, as he was in a position of relative safety for the immediate future.

3.) The Battle of Gettysburg

Robert E. Lee had just seen victory against the Union army at Chancellorsville and now had his sights set on the long-awaited invasion of the North. Gettysburg was chosen as the battlegrounds, and it was there that Lee was met with incredibly stiff resistance.

The Battle of Gettysburg commenced, lasting from July 1-3, 1863. Massive casualties were taken by both sides in what soon proved to be one of the bloodiest battles of the entire war.

Lee marched into the fray with an estimated 75,000 men. By the end of the third day, Lee had lost 28,000 men, leaving him with 63% of his original fighting force. This meshes almost perfectly with the Golden Ratio of 0.618.

Lee was forced to retreat from the battlefield, and for the South, the Civil War was largely over. From Gettysburg onwards, the South would fight a defensive war as the North tightened its grip on victory.

2.) Operation Barbarossa – When Time was Golden

Hitler wanted the German people to have more “living space” and, in his quest for doing so, put through Operation Barbarossa – the Nazi invasion of Russia – on June 22, 1941.

Roughly two years of German offensive action followed, with the Soviets unable to mount much of an effective response. Hitler divided his men into three separate prongs of his attack. While 41 divisions were sent to the south and 52 were sent to the center (making a total of 93 divisions), only 29 divisions were sent to the north – a third of the combined strength sent below them.

Repeated blunders left the Nazis locked in battle at Stalingrad, which is readily recognizable as the turning point of Operation Barbarossa. It was in November 1942 the German offensive into Stalingrad quickly soured into a defensive battle. This turning took place in the 17th month of the German invasion of Russia, marking the “golden point” of the 26 months during which the German attack turned into a defensive war against the ever-growing Red threat.

1.) Gold in the Desert – Operation Desert Storm

As Saddam Hussein invaded Kuwait in what was the beginning of the Gulf War, he never imagined the storm which would quickly follow.

Expecting widespread support for his actions amongst the Arab League, Hussein was surprised to discover that 2/3 of the League actually condemned what he had done.

Things heated up for Hussein as the US issued the ultimatum to evacuate Kuwait by January 15, 1991, or to face overwhelming force. Hussein, of course, refused, and Operation Desert Storm began. General Schwarzkopf of the US believed that timely battlefield communication was key to winning this war with minimal loss of American life, instituting widespread intelligence changes throughout the US Army.

Aside from deploying the first UAVs in combat, Schwarzkopf also saw to it that three military intelligence brigades were now deployed with two Army corps (a 2:3 ratio) as well as with one field army.

Further use of the Golden Ratio at work can be found in that the Iraqi Republican Guard finally fell after 38% of it had been destroyed. With approximately 62% of its original fighting force left (eerily close to the 0.618 of the Golden Ratio), the Republican Guard fell, and the Gulf War was over.

The Point

If the golden ratio works in art and it works in military history, can it also be applied to other things? Can you find ways to put it to use for prepping? Does it mesh well with your disaster communications plan? Mike Shelby of Forward Observer (which you should subscribe to) is constantly talking about performing an area study. Can the golden ratio be applied to that? What about with your bug-out bag food? Will you get the most calories and the best nutrition for the weight if you apply the golden ratio?

These are just a few examples to get you thinking.

I don’t want you to jump on the Jim Carrey (bleck) The Number 23 bandwagon here thinking that this is somehow a magical formula or anything stupid like that. But, just like there are basic mathematical principles that work with architecture, there may be other ones that work with other things.

(Also, I’ll point out that I wasn’t the one that made this discovery. The Chinese mentioned it back in 1998 in their army manual Unrestricted Warfare. I just looked for other examples in military history where the golden ratio could be found in use.)

What are your thoughts on all this? Do you think this is interesting, or is it a sideshow gimmick of a number? Do you try to incorporate it into different aspects of prepping? Is it something you’ve applied to any facet of your life? Let us know your thoughts in the comments section.

About Aden

Aden Tate is a regular contributor to TheOrganicPrepper.com and TheFrugalite.com. Aden runs a micro-farm where he raises dairy goats, a pig, honeybees, meat chickens, laying chickens, tomatoes, mushrooms, and greens. Aden has four published books, What School Should Have Taught You, The Faithful Prepper,  An Arm and a Leg, The Prepper’s Guide to Post-Disaster Communications, and Zombie Choices. You can find his podcast The Last American on Preppers’ Broadcasting Network.