Prince William and his son Prince George have many things in common: a patriotic duty to the nation of their birth; an intimate working knowledge of Kate Middleton's breasts; a high risk of hemophilia. Between them, they also have enough hair to cover the head of one human male.

Indeed, George is quickly gaining hair while William is losing his at a similar rate, and experts agree that we are rapidly approaching the moment when 31-year-old Prince William and his eight-month-old son will have exactly the same amount of hair on their crowns—a hypothetical date referred to as "Hair Equilibrium." (See Fig. 1)

Fig. 1: Trend lines, amount of hair across time. Data visualization by Jim Cooke.

But when exactly will it happen? Recent photos of the Cambridge family touring New Zealand, plus advanced data-modeling techniques, have allowed us to predict Hair Equilibrium to the date. Here are the facts:

FACT: Prince George has much more hair on top of his head; enough for a soft baby fauxhawk to form in the breeze. Prince William has far denser coverage on the sides. (See Fig. 2)

Fig. 2: Side-by-side comparison. Images via Getty.

FACT: Prince George has finer but more even coverage overall, facilitating the implementation of a subtle combover. Prince William can no longer pull-off a successful combover. (See Fig. 3)

Fig. 3: Combovers, compared. Images via Getty.

FACT: An average baby's head has roughly 1,100 hair follicles per square centimeter. The typical circumference of an English infant's head at eight months is 44.5 centimetres (SI units only, please).

The surface area of a sphere is calculated by 4πr^2

C = 2πr

44.5 cm = 2 x 3.14 x r

22.25 = 3.14 x r

7.06 = r

4 x 3.14 x (7.06 x 7.06) = 625.99 ≈ 626 cm

626 x ⅗ of head covered by hair = 375.6 cm

375.6 cm^2 x 1,100 follicles per square cm = 413,160 individual hairs (rough calculation).

FACT: An average 30-year-old man's head has roughly 300 hair follicles per square centimeter (300 hair follicles per square centimetre, English).

The typical circumference of a 30-year-old male's head is 57 cm.

57 cm = 2 x 3.14 x r

28.5 = 3.14 x r

9.08 = r

Surface area = 4 x 3.14 x (9.08 x 9.08) = 1035.5 ≈ 1036 cm

1036 x ⅗ of head covered by hair = 621.6 cm

621.6 cm x 300 follicles per square cm = 186,480 individual hairs (rough calculation)

Does this mean that Hair Equilibrium has already been reached? Even an amateur unassisted by cutting-edge hair-counting technology can see in the images above that William has more hair, particularly on the sides.

∴ (therefore) flip the numbers

∴ Prince George has 186,480 individual hairs and Prince William has 413,160 individual hairs currently.

FACT: Hair grows faster in summer than winter, by a rate of millimeters.

It is currently autumn in New Zealand.

Autumn occurs between summer and winter. HOWEVER, Autumn:Winter::Spring:Summer.

Both sets of hair are currently growing the regular(?) amount.

FACT: The average person loses 50 to 100 hairs per day. Prince William has been alive since June 21, 1982. Prince George has been alive since July 22, 2013. Today is April 10, 2014.

∴ Over the course of 11,617 days, Prince William has likely lost between 580,850 and 1,161,700 hairs. Over the course of 263 days, Prince George has likely lost between 13,150 and 26,300 hairs. Infants often lose all their hair shortly after birth ∴ x 10 = 131,500 - 263,000.

HOWEVER in New Zealand it is already April 11, 2014, ∴ this math is invalid.

FACT: Prince William has been losing hair rapidly since the birth of his son last July, probably due to a combination of stress, genes, and the mystical laws of the universe that govern the ascension of the coven Supreme. (See Fig. 4)

Fig.4: Left: July, 2013; Right: April, 2014. Images via Getty.

IRONIC: A baby with all the money in the world can't buy the one thing he craves more than anything: the confidence and joie de vivre that only a naturally thick head of hair can provide. (See Fig. 5)

Fig. 5: Longing. Image via Getty.

FACT: Heavy is the head that wears the crown.

FACT: Prince George was born on a Monday. Monday's child is fair of face.

Prince William was also born on a Monday, HOWEVER a partial solar eclipse occurred on his birthday, ∴ invert poem, ∴ Monday's child: hair misplaced.

FACT: There are seven letters in "William"; six in "George"; four in "hair."

7/4 = 1.75 ≈ 1.8 ≈ 2

6/4 = 1.5 ~ 2

2 ≈ 2

∴ William = George

Upload this collection of figures and data to the cloud by pressing SHIFT + fn + 4:

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Prince George and Prince William will achieve hair equilibrium on Friday July 11, 2014.

So there you go.