Markham data lessonMeasuring 3,424 Markham trail segments with the distance formula
The City of Markham publishes its Trails layer as open data: each piece of trail is a list of coordinates in metres, stored with the City’s own LENGTH value. We computed every length ourselves and compared. The results below are our calculations.
The City describes the layer as trails within Markham used for walking and hiking. Its coordinates are in a projected system, UTM zone 17 north, where x and y are measured in metres east and north. That matters for a student: in a projected grid, the length of a short straight piece really is the square root of (change in x) squared plus (change in y) squared, the same formula taught in Grade 10. On a map in latitude and longitude it would not be.
Our checks on the City of Markham Trails layer, downloaded 22 October 2026| What we checked | Our result |
|---|
| Segments in the layer | 3,424, each with its own OBJECTID and geometry |
| Our length within 1 cm of the LENGTH field | 3,240 segments |
| Our length within 1 m of the LENGTH field | 3,422 segments |
| Largest disagreement | OBJECTID 3066: ours 41.21 m, stored 44.92 m, a gap of 3.70 m |
| Second largest | OBJECTID 3064, a gap of 2.99 m |
| Median segment length | 36.7 m (mean 72.4 m, longest 3,139.6 m) |
| Surface field, most common values | CONC 1,348, ASPH 1,250, GRAV 420, blank 224 |
| Marked public in the PUBLIC_ field | 3,033 Yes, 377 No, 14 blank |
A segment is not one straight line but a chain of short ones, so its length is the sum of the distance formula over each pair of neighbouring points. The program below does exactly that for every segment, then counts how often our answer agrees with the City’s stored value. It uses only Python’s standard library; math.dist is the distance formula written for you:import json, math
def polyline_length(paths):
total = 0.0
for path in paths:
for a, b in zip(path, path[1:]):
total += math.dist(a[:2], b[:2])
return total
segments = []
for name in ("trails_page_0.json", "trails_page_2000.json"):
segments += json.load(open(name))["features"]
gaps = []
for seg in segments:
ours = polyline_length(seg["geometry"]["paths"])
gaps.append((abs(ours - seg["attributes"]["LENGTH"]), seg["attributes"]["OBJECTID"]))
print("segments:", len(gaps))
print("within 1 cm:", sum(g < 0.01 for g, _ in gaps))
print("within 1 m:", sum(g < 1 for g, _ in gaps))
print("largest gaps:", sorted(gaps, reverse=True)[:2])
Agreement is evidence
Our formula and the City’s field agree to the centimetre on 3,240 segments. That is strong evidence the stored lengths are flat, two-dimensional lengths on the same grid, not lengths along the slope of the ground.
Disagreement is a question
Two segments are off by about three metres. The file does not say why, so we do not guess. A student should report the gap, show both numbers and say which further check would settle it.
Mean against median
The mean segment, 72.4 m, is about twice the median, 36.7 m, because a few long segments stretch the average. Most pieces of a trail network are short.
Licence and attribution
Contains public sector Information made available under the City of Markham’s Open Data Licence (licence). The lengths, comparisons and counts on this page are ours. The City of Markham does not endorse this page or our classes. We print no total trail length, because adding the City’s segment lengths would only restate their numbers.
