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Home » The Forbidden Touch Revealed—What Happens When You Break the Rules of the Anointed! - Dachbleche24

The Forbidden Touch Revealed—What Happens When You Break the Rules of the Anointed! - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Pick’s Theorem states:

📌 A = I + \frac{B}{2} - 1

📌 where $A$ is area, $I$ is interior lattice points, and $B$ is boundary lattice points. We seek $I$, but the problem wants interior points only. First, compute the area of the large equilateral triangle with side length $6$:

📌 A = \frac{\sqrt{3}}{4} \cdot 6^2 = \frac{\sqrt{3}}{4} \cdot 36 = 9\sqrt{3}

📌 Now, determine $B$: the number of lattice points on the boundary. Each side has $6 + 1 = 7$ points, but corners are shared. Since it’s a triangle,

📌 B = 3 \cdot 7 - 3 = 21 - 3 = 18

📌 Now apply Pick’s Theorem:

📌 9\sqrt{3} = I + \frac{18}{2} - 1 = I + 9 - 1 = I + 8

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2x^2 + 35x - 175 = 0
Using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}...
a = 2, \, b = 35, \, c = -175
x = \frac{-35 \pm \sqrt{35^2 - 4 \times 2 \times (-175)}}{4}
x = \frac{-35 \pm \sqrt{1225 + 1400}}{4} = \frac{-35 \pm \sqrt{2625}}{...
\sqrt{2625} \approx 51.23
x = \frac{-35 \pm 51.23}{4}
Taking the positive root:
x = \frac{16.23}{4} \approx 4.0575
#### Width of walkway: Approximately 4.06 meters

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