✨ Exact BMI Reverse Calculator - Find Minimal Height/Weight
Based on prime factorization, reversely calculates the exact minimum height and weight for a target BMI without floating errors.
💡 Supports integers, decimals, or fractions. Math engine assumes weight is accurate to 0.1kg and height to 0.001m.
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The Beauty of Mathematical Modeling
The BMI formula is $B = \frac{w}{h^2}$. Assuming weight $w$ has 1 decimal place and height $h$ has 3 decimal places, we get:
$W = \frac{P \cdot H^2}{10^5 \cdot Q}$
For $W$ to be a positive integer, the denominator must divide the numerator. By performing prime factorization on the simplified denominator $D$, we ensure $H$ contains the required primes, achieving a perfect reverse calculation.