The Geometry of Flight: Zodiac’s Movements Mapped Through Cartesian Logic
The November 9, 1969 “Bus Bomb letter" contains several spatial assertions about the Zodiac Killer’s movements inside the Presidio on the night of Paul Stine’s murder. These statements are often treated as narrative impressions, but when interpreted as literal measurements - distances, directions, and block counts - they form a coherent geometric system. That system is best understood as a Cartesian coordinate reconstruction, anchored to the straight street grids bordering the Presidio. Once framed this way, the constraints converge on a single, topographically consistent hiding location inside the park.
Three statements in the letter provide the strongest locational constraints: Zodiac’s claim that the police dogs never came within two blocks of him, his description of disappearing into the park a block and a half away, and motorcycles passing approximately 150 feet away, traveling from south to northwest. These are directional and measurable. When placed into a coordinate system, they sharply limit the region in which he could have been concealed.
A Cartesian system requires straight, orthogonal reference lines. West Pacific Avenue, which borders the Presidio, is curved and sloped; it cannot serve as a reliable baseline for estimating blocks. The first straight east–west street south of the park is Pacific Avenue from the point of Walnut Street eastward, and the first straight north–south street he is encountered is Maple Street. These two streets form the necessary X–Y axes. They provide the straight, perpendicular lines required for estimating both the “two blocks” separating him from the dog teams and the “block and a half” he claims to have walked into the park.
The dog‑search coordinate is the first anchor point. Although the police dogs were deployed at Julius Kahn Playground, the relevant geometric point is not the playground entrance itself. Instead, it is the point where the Pacific Avenue line intersects the entrance path just north of the Julius Kahn entrance. This point lies directly on the Pacific Avenue axis and serves as the center of the two‑block radius - approximately 580 feet, based on the 290‑foot block length in the neighborhood East of the Presidio. When that radius is drawn, the resulting circle extends westward into the Presidio, extends nearly to the Maple Street axis, and reaches just far enough north that its edge approaches the Lower El Polín Spring, just below the El Polín Loop. It does not extend into the basin where Zodiac ultimately hid. This geometry aligns precisely with his statement that the dogs were “to the west” and never came within two blocks of him. He just didn't say that they were south.
The second coordinate is the 1.5‑block disappearance point. After leaving the cab at Washington and Cherry, Zodiac walked north to Jackson, east to Maple, and then north towards the Presidio. The point where Maple Street meets the Pacific Avenue axis becomes the center of the 1.5‑block radius - approximately 435 feet. When that radius is drawn, its northern edge falls right at the edge of the shallow basin south of El Polín Spring, a visually shielded interior zone consistent with concealment. This point, like the dog‑search coordinate, lies on the same straight Pacific Avenue axis, but farther west along it. The two circles therefore share a common east–west baseline while representing distinct spatial constraints.
The most decisive directional constraint is the motorcycle passage. Zodiac wrote that the motorcycles went by about 150 feet away, traveling from south to northwest. In this portion of the Presidio, only one feature matches that bearing: Lower Ecology Trail. It runs diagonally from the south toward the northwest, cutting across the interior of the park. The distance between Lower Ecology Trail and Lower El Polín Spring is approximately 335 feet. The midpoint - about 167 feet - corresponds closely to Zodiac’s “150 feet” estimate. This places him east of the trail, south of the springs, and positioned within the wooded depression between them.
When the constraints are treated as coordinate boundaries - two circles of fixed radius anchored to the Pacific Avenue axis, a directional vector, and a known origin - the solution space collapses to a single, narrow region. The pocket of land between Lower Ecology Trail and Lower El Polín Spring satisfies all conditions simultaneously. It is north of Maple Street, just beyond his self‑reported 1.5‑block limit, outside the dogs’ two‑block radius, west of the dog team starting location, north and east of where he noted noticing them to the west and situated so that motorcycles on the trail would pass at the distance and direction he described. It is also a location with symbolic resonance, consistent with Zodiac’s tendency to embed meaning into geography. However, that is for a later article.
This reconstruction does not rely on speculation. It relies on the properties of a Cartesian coordinate system: straight axes, fixed radii, measurable distances, and directional vectors. When Zodiac’s statements are interpreted through that framework, they converge on a single place where he could have concealed himself, listened, and observed as police activity unfolded around him.
This article is Part One of a two-part article. Check back later for Part Two.