On Capitol Hill, the House of Representatives has passed articles of impeachment, charging the president with abuse of power and obstruction of Congress. At the White House, the president’s aides call the impeachment a sham and argue that it is congressional leaders who are guilty of abuse. Neither side is likely to prevail in this standoff. Yet neither side will concede an inch.

The impasse dominates the news cycle, boils over on Twitter, pits blue states against red and spills onto the international scene. Yet in reality, the confrontation is taking place in a remarkably confined space. The White House and Capitol Hill are exactly one and a half miles apart, connected by Pennsylvania Avenue. The tug of war that is shaking the nation and the world is taking place between opposite ends of a single boulevard that runs through the heart of Washington.

The pattern doesn’t end there: You can draw one line from the middle of the Capitol building through the Mall, and another line southward from the White House through the Ellipse, and the two lines will intersect at an exact right angle. The poles of impeachment are also two corners of a precise right triangle.

This might seem like an odd bit of D.C. trivia, which might dazzle a mathematically inclined tourist but few others. In fact, the opposite is true: The geometric design was put there to represent our constitutional order, in which coequal branches of government are ranged against each other in an inherent tension, resulting in ultimate stability.

As outlined in the Constitution, the president and Congress would serve as a check on each other’s power, neither allowing its rival to encroach on its exclusive domain. And yet together they would harmonize to forge a unified government. To James Madison, chief architect of the Constitution, this arrangement was not simply practical. It was also, he explained in the Federalist Papers, possessed of “symmetry and beauty of form.”

It was these aesthetic qualities that the capital’s French-American designer, Pierre Charles L’Enfant, set out to imprint upon the federal capital when he was appointed to his position in 1791. And for him, as for many of his contemporaries, symmetry and beauty could mean only one thing: The design must be grounded in the principles of geometry.

As the son of a court painter to King Louis XV, L’Enfant grew up in France’s royal court, dividing his time between numerous royal palaces and castles. Nearly all of these possessed vast and exquisitely manicured gardens, delicately trimmed into precise geometrical patterns. Yet none could match the most glorious of them all, the gardens of Versailles, created by Louis XIV’s chief gardener, André Le Nôtre.

Le Nôtre had created a complete world of forests and meadows, flowers and springs, and even (for a while) oceangoing ships and wild animals. It was a beautiful, flourishing, colorful garden but also one that was precisely arranged into lines, circles, triangles and squares. In Versailles’ orderly geometrical kingdom, everything was exactly in its place.

And at its summit was the looming presence of the shining palace on the hill. All straight paths converged on it, all geometrical patterns pointed only to it, and all lines of sight and power flowed from it. The garden’s geometry upheld the supremacy of the kings of France.

When L’Enfant sailed to America in 1777 to fight for the new United States, he carried the vision of Versailles with him. And when 14 years later, he sat down to design the new federal capital, it was Le Nôtre’s garden that was foremost in his mind. Indeed, when viewed in isolation, the Mall (which L’Enfant called a “Grand Boulevard”), sloping down from Capitol Hill, bears precisely the same relationship to the houses of Congress as the gardens do to the palace at Versailles. In both, broad and straight boulevards converge in a symmetrical pattern on the great palace, which rules all from its perch at the top of the hill. The supremacy of the people’s representatives, like the rule of the king of France, was symbolized and supported by the geometry of the physical space.

Unlike Le Nôtre, whose goal was to represent royal supremacy, L’Enfant sought to show how competing centers of power balanced against each other. Today we would undoubtedly consider the Supreme Court to be one of the key nodes, but in 1791 it was still decades removed from being a coequal branch of government. The true check on congressional power came from the presidency, and L’Enfant set out to represent it as such. He outlined another great park sloping southward from “The Palace of the President,” with its own straight lines and geometrical patterns attesting to the president’s power.

The powers of Congress and the presidency, in L’Enfant’s design, were neither independent nor simply opposed, but rather rectilinear to each other. The presidential park (which today includes the Ellipse and the South Lawn) intersects with the Mall at a right angle, which L’Enfant suggested should be marked by an equestrian statue of George Washington. From there, just west of where Washington Monument now stands, one can look northward, to the White House, or eastward, through the Mall to Capitol Hill. To complete the pattern, the two nodes of power are connected by a straight and broad boulevard that L’Enfant designated Pennsylvania Avenue. It forms the hypotenuse of the constitutional triangle.

The constitutional right triangle at the heart of Washington is symmetrical, even beautiful, just as Madison would have hoped. But it is also strong. For the sides of a triangle hold each other tightly in place, its corners locked in an immovable relationship to each other. In this geometric construction, Congress and the president, positioned in the corners, are bound to each other yet unable to infringe on the other’s position. The branches of the government push against each other in a dynamic and irresolvable tension, yet join to form a balanced and harmonious whole. And all of it is founded on the perfect order of geometry.

In normal times, the strict geometry of our constitutional order is largely hidden from view, as the government of the country proceeds by softer means. The give-and-take between rival interests, and the occasional joining-together in times of crisis, play a far greater role in day-to-day governance than careful constitutional balance laid down by the framers. They are exchanges founded on trust, and the conviction that beneath the stormy surface of our differences lies a deep ocean of shared values.

Yet in today’s America, trust is in short supply, as Americans regard each other with suspicion and contempt. As the impeachment process grinds forward, and the House of Representatives is pitted against the White House in a balance of mutual paralysis, the facade of cooperation is slipping away, exposing the cold geometrical skeleton of our government. This may not be exactly what Madison had in mind when he extolled the “symmetry and beauty of form” of the constitutional order. But at a time when so many of the ties that bind us together are fraying, it is something to hold on to. The geometrical Constitution, written into the streets of our capital, still holds.


Amir Alexander teaches history at the University of California, Los Angeles, and is the author of “Proof!: How the World Became Geometrical.” He wrote this article for the Washington Post.