Know how common a gene is, and you know how common each pairing will be — with no evolution at all, the genotypes settle into p², 2pq, q². It is the null hypothesis of genetics: what a population looks like when nothing is happening. Slide the allele frequency (or tap).
The Hardy–Weinberg principle. If an allele A has frequency p and a has q=1−p, then under random mating with no selection, drift, migration or mutation the genotype frequencies are AA=p², Aa=2pq, aa=q² — and they sum to exactly (p+q)²=1. Heterozygotes are most common at p=0.5 (2pq peaks at 0.5), and a rare recessive allele hides overwhelmingly in carriers rather than affected homozygotes. It is genetics' null model: departures from p², 2pq, q² are the signature that something — selection, drift — is acting. The three parabolas and the current split are drawn live; a fail-loud self-check throws unless the frequencies sum to 1 and the heterozygote fraction is maximal at p=0.5.
The idealised infinite, randomly-mating population with no evolutionary forces; real populations deviate (that is the point of the test). The p², 2pq, q² identities are computed exactly.