Kardioidi

Kardioidi is a term used to describe heart-shaped curves and related directional patterns in mathematics, acoustics, and radio engineering. The name derives from Greek kardia, heart, and eidos, shape, and is used in several languages to refer to cardioid forms and patterns.

In mathematics, a cardioid is a plane curve with a single cusp. It can be generated as the epicycloid formed when a circle of radius a rolls around another circle of the same radius. Its polar equation is r = a(1 − cos θ), and a common parametric form is x = a(2 cos t − cos 2t), y = a(2 sin t − sin 2t). The curve is symmetric about the x-axis, has a cusp at the origin, and encloses an area of (3/2)πa^2.

In acoustics, a cardioid microphone pattern (often termed a kardioidi in some languages) describes a directional sensitivity that is strongest at the front and has a null at 180 degrees. This pattern reduces pickup from the rear, improving signal-to-noise in noisy environments. It is typically realized with a pressure-gradient design or with electronically combined capsules that create the characteristic frontal lobe and rear null.

In antenna theory, cardioid patterns can be produced by combining signals from multiple elements with appropriate amplitude and phase, yielding a directional radiation or reception pattern with front emphasis and rear suppression. Cardioid concepts also inform related patterns such as supercardioid and hypercardioid.

See also: cardioid, epicycloid, polar coordinates, microphone pattern, directional antenna.