Which parallel divides landmass in half?

Question

We know that 67.3% of land mass is in the northern hemisphere, and 32.7% in the southern. Now we go towards the north from the equator. On which parallel the amount of landmass north of it and south of it is equal?

Answer 1

Roughly half the land on Earth is north of the Tropic of Cancer (23°N).

To estimate this, I just modified the code used by @MyCarta in their answer to "In the northern hemisphere only, what percentage of the surface is land?". Using a Peters equal projection map of the world from Wikipedia, I counted the total land pixels and then found the row in the map array which divided them in half. I then converted pixel row in the map array to a latitude using the inverse of the Peters y projection formula. Here are maps showing the northern and southern halves of the Earth's land.

Here is my (quick and inelegant) code:

import numpy as np
from skimage import io
from matplotlib import pyplot as plt

# Load equal area projection map from wikipedia
url='https://upload.wikimedia.org/wikipedia/commons/e/e2/Peters_projection%2C_black.png'
total_equal_area =io.imread(url, as_gray=True)

equal_area=total_equal_area

# Get shape and size of map
rows, columns = np.shape(equal_area)
total_area = rows*columns
print("Rows and columns in map: ", rows, columns)

ocean_area  = np.sum(equal_area)
land_area = total_area - ocean_area

print("Total pixels in map: ", total_area,
      ";   Land pixels in map:  ", int(land_area),
      "\nFraction of pixels representing land:",
      np.round(land_area/total_area*100, decimals=2))

n=386
equal_area_n=total_equal_area[:n, :]

r_n, c_n = np.shape(equal_area_n)
total_area_n = r_n*c_n
print("Cutoff row: ", r_n, ";  Total land pixels above this row: ",total_area_n)

ocean_area_n  = np.sum(equal_area_n)
land_area_n   = total_area_n - ocean_area_n

# Convert rows to latitude using Pinvers of Peters y formula from
#   https://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection#Formula
latitude_n = np.degrees(np.arcsin(1-2*n/rows))

print(np.round(total_area_n/total_area*100, decimals=1),
      "% of the Earth's total surface area and ",
      np.round(land_area_n/land_area*100, decimals=1),
      "% of the Earth's land area is North of Latitude: ",
      np.round(latitude_n, decimals=1),"°N", sep='')

# Plot map of area containing 50% of Earth's land
fig = plt.figure(figsize=(20,10))
ax  = fig.add_subplot(1,1,1)
ax.set_xticks([])
ax.set_yticks([])
plt.imshow(equal_area_n,cmap='gray')