When it comes to horseback riding, it’s easy to disregard geometry. But, beyond the beauty of forward motion, the expertise of equitation and the exquisite engine that is the saddle horse, the art of mathematics shapes what we create between the ears.
And by “shapes” we mean that quite literally.
The circle may be the most profound shape of riding. The round chord, where all curved lines are equal distances from the center point, is so much more than a shape. It’s a test of contact, an indication of awareness, and an understanding of consistent rhythm. Circles build confidence and strength. Horse and rider must be subtle, stride by stride, with cues and adjustments.
The circle defines patience, precision and bend. On horseback, the circle becomes art.
So, what makes a circle? Circles represent wholeness and a natural sense of completion. The rider bends the horse’s body laterally and ensures the horse tracks its hind feet in exact accordance with the front feet.
The shape itself is fundamental to all disciplines, especially saddle seat. According to Enid Norton in an excerpt from a Mountain View Stables collection of research called “Saddle Seat Equitation According to Enid Norton,” the saddle seat equitation discipline is “filled by variable norms and forms while being judged on imaginary shapes and lines.” Riding “is fueled by an inexplicable desire to achieve the almost impossible while relying on the idea that your interpretation of sound horsemanship practices … and execution of precision and perfection, are enough.”
In a competitive equitation pattern, the circle tests rider proficiency. A perfect circle enhances horsemanship ability because it’s the ultimate test of the animal’s direction, gait and speed. And the rider’s ability, too. Perfecting a circle in the pattern should be shown with maximum effectiveness and minimum effort.
Outside of the equitation pattern, riders that don’t space themselves correctly attract negative attention. The circle is a calculated decoy, so the flow of the ring is not interrupted. For assistance later in the show ring, riding circles will help improve the rider’s ability to utilize corners and ride accurately. As the rider learns to feel a balanced horse, they can use their leg, correct on their own, and ride steady corners into the straightaway.
Much like saddle seat, in dressage the circle is a prerequisite movement for movements that come later. Alison Sader Larson, a nationally renowned dressage trainer, graduate of the USDF ‘L’ program, and USDF medal recipient, stresses the importance of perfecting the movement.
“If you’re not able to ride a forward bending circle, it’s going to be hard to do a half pass later on,” she said. “It initiates lateral flexion throughout the body and bending around that inside leg, and in that response, it helps loosen up the horse.”
In equestrianism, specifically dressage, lateral flexion has a unique meaning. Lateral flex is a movement made by a horse where the animal is moving in a direction other than straightforward. To get really technical, the flex is different than the bend, because a bend requires the entire horse’s body. Meanwhile, a flex is a movement of the head. Lateral flexion is the first part of a circle, which initiates the bending of the entire body, and essentially teaches the horse to move away from the rider’s leg pressure. To put it figuratively, lateral flexion is the seed of a beautiful, blooming circle.
Even more, flexibility is a crucial component of achieving lightness in the bridle. A heavy horse is often poorly conditioned or tense. Circles can help alleviate both. On the left circle, this means pushing the horse’s left shoulder and ribcage to the right, asking to soften their neck and jaw, and keep momentum. Their shoulders and hind end should follow their front end, and their face should actively propel forward. Hips should not “drift” outside the circle and instead follow the arc like a thread.
Circles have multiple benefits. For the horse, the shape develops symmetry in the spine and stabilizes its muscles. The curvature creates flexibility through the horse’s trunk and helps them learn to find balance. Many of us know a circle can help calm down an emotional horse; center their mind. Essentially, circles also help us take a moment to regroup and reposition.
“Horses have a generalized thought process and reaction to circumstances,” Enid Norton writes. “Different horses will all react in the same manner during testing segments due to the nature of their natural mindset. It is important to understand how a horse’s thought processing functions and to prepare accordingly.”
Moreover, if the horse constantly engages in an incorrect circle, its muscles will become accustomed to that inaccurate shape and no gains are made in those postural muscles. The rider, too, becomes lazy.
So, what’s the key to riding the perfect circle? Alison believes it starts with balance and (you guessed it) math.
“If you don’t have the horse in balance bending, going forward, and turning towards the outside rein, it’s going to be hard to ride the circle,” she said.
That’s where the geometry comes in.
“The rider has to know what a circle looks like,” she said. “How far is the distance from the corner to H? From H to S? You need to know what makes a 20-meter circle in diameter. You need to know that 6 + 12 is 18 to the next line. Unfortunately, a lot of people do not know the actual distances between their letters. Especially when you go from a large arena to a small arena. People seem to ignore that quite a bit. This part is very important.”
In saddle seat, when horses come out of the corner and drive the straight line down the rail, circles will give them the equipment to have controlled impulsion, headset and motion. Instead of leaning on the bridle, horses will engage their hind end, follow their head and drive forward.
That power derives from the horse’s ability to balance and not cheat corners.
“The rider needs to keep the horse bent on the curvature line through its entire frame,” Enid writes. “And maintain the horse's balance, preventing a closed or open shoulder from the horse in the circle. The circle should present equal depth through all four of its quarters.”
Riding a circle is, of course, harder than it looks. Riders will accidentally ride an egg shape, a square, something that doesn’t resemble something round at all. The horse will overbend in the face and neck, rubberneck or pull its head around too far. The rider will lose balance, fall into the outside, and become crooked, so the horse becomes crooked. Even more, riders will take their horse too deep into the corners and lose their consistent speed.
So how can we get away from egg-shaped figures and inconsistent speeds? Many trainers find that riding circles without structure doesn't necessarily improve them. Mathematics are, indeed, the answer.
“In the execution of a circle, once the circumference has been determined, divide it into quarters to ensure equal striding/size,” Enid writes.
Correct positioning can lend a hand to riding a proper circle as well. In dressage, it's all about hip placement.
“Your shoulders and hips should be in line with the horse,” Alison said. “So, the bend of the horse's body and the amount you’re turning your body is more if the circle is smaller. The reins and the legs are a little more complicated. The hands are even, inside rein slightly shorter because the horse's neck should be shorter if bending correctly. The inside leg is a hair forward. As far as bending, I don’t need too much leg to make the circle.”
For less experienced riders, longe lessons with a compliant school horse teach them how to rebalance away from their hands and center their seat. This self-control away from the reins and stirrups teaches the “feel” of a centered seat and helps the rider understand the correct circle bend. Eventually, riders won't “over ask” for the arc.
Jennefer and Mya Lear, trainer and assistant trainer at Willow Falls Farm alongside trainer, Dave Hysaw, stress the importance of keeping an eye on your center.
“The first time around, look for points to count strides between,” Jennefer said. “Keep even weight in each stirrup; adjust if you’re tipping in.”
“There is no end or beginning of a true circle and the shape should reflect that,” Mya added. “There are no corners or sharp turns or straight lines. That’s the biggest mistake I see riders make.”
An extra tip? Variation.
“The benefit of practicing in lessons (especially equitation) is practicing different size circles,” Jennefer said “That keeps you riding each step rather than going around and around trying to have a perfect position. A strong position is important, but a strong rider is the goal.”
In the end, circles aren't as simple as they appear. Perhaps that’s the beauty of their continuous practice. Circles are balance, completion and symmetry. They require the horse to be obedient and engaged. They teach the rider to be accurate and precise, subtle in cues, and centered in the saddle.
Just like a piece of art, circles help us center ourselves and realize why we love the sport in the first place. Why? They’re the center point of what we do every day; the commonality of their practice is a benefit for every rider.
“I love to spiral in, spiral out,” Alison said. “I use counter-bending work, and haunches in. Canter work on the circle. There’s so much that can be done [in the circle]. That’s what I really like about it. I can teach and train so much and never leave a circle.”
Perfect circles, stronger riders. Now that’s an art.