Riverdale Robotics
Pandamonium
FRC Team #2915

English Español Français 日本語

What is that crazy formula doing there? you may be wondering. It's there because it's our team number. To show why, let's take it step by step.

(⌈ζ(2)⌉² (9C5 − 4(57b8 mod 7)²) √(1 − cos² π/3!) − e^iπ ))∫(cot π/4, e¹¹) 1/x dx W(Σ(n=1, ∞) 9/10ⁿ, x, x⁵) / 4x³ − δ⁻¹(1/{ℕ|})

ζ is the Riemann zeta function, which is defined as ζ(s) = 1/1^s + 1/2^s + 1/3^s + .... ζ(2) is equal to π²/6, or approximately 1.645.

⌈x⌉ is the ceiling ("round up") function; it returns the least integer not less than x. ⌈ζ(2)⌉², then, is equal to 4.

(9C5) is a binomial coefficient, defined as (nCk) = n! / k!(n−k)!; (9C5) therefore equals 126.

57 in octal (base 8) equals (5 × 8 + 7) = 47 in decimal. 47 mod 7 is equal to the remainder of 47 ÷ 7, which is 5.

By the Pythagorean identity, 1 − cos² x = sin² x. Since 3! = 6 and sin π/6 = 1/2, √(1 − cos² π/3!) = √(1/4) = 1/2.

Euler's identity states that e^iπ + 1 = 0; e^iπ, therefore, equals −1.

So the contents of the first set of parentheses evaluate to (4 (126 − 4 × 25) 1/2 − −1) = (4 (126 − 100) 1/2 + 1) = 53.

cot π/4 = sin π/4 / cos π/4 = √2 / √2 = 1, and ∫ 1/x dx = ln x + C, so ∫(cot π/4, e¹¹) 1/x dx = ln e¹¹ − ln 1 = 11 − 0 = 11.

Σ(n=1, ∞) 9/10ⁿ = 9/10 + 9/10² + 9/10³ + ... = .999... = 1 (proof). The Wronskian is

Wronskian

and therefore

W(1, x, x⁵).

1/{ℕ|} is a surreal number—specifically, it is the reciprocal of the smallest ordinal larger than all natural numbers, which is commonly denoted ε. The Dali function, δ, is a mapping from the real numbers to the surreal numbers. Inverse Dali, therefore, maps surreals to reals, so δ⁻¹(1/{ℕ|}) is the nearest real number to ε, which is zero.

The whole formula, then, evaluates to 53 × 11 × 20x³ / 4x³ − 0 = 53 × 11 × 5 = 2915.