← All parts of this equation

Equation 1 · Part 10 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

Numerator: dvarphi

M(q)=dφdq,v(t)=M(q(t)) i(t)M(q) = \frac{d\varphi}{dq}, \qquad v(t) = M\big(q(t)\big)\, i(t)
dφd\varphi

What this part means

The complete quantity above the fraction bar.

Its job in the formula

dvarphi occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

In 1971, Leon Chua published “Memristor — The Missing Circuit Element” in IEEE Transactions on Circuit Theory . His argument was one of pure symmetry, not empirical discovery. Circuit theory recognizes four fundamental variables — charge, current, voltage, and magnetic flux linkage — and, in 1971, three of the six possible pairwise relationships among them were already embodied in named components: the resistor relates voltage and current, the capacitor relates charge and voltage, the inductor relates flux linkage and current. Chua noticed that the sixth relationship, between charge and flux linkage, had no corresponding physical device, and reasoned from the completeness of the other five…

Read this part in the article →

Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.