Abstract: An expandable joint for use in, for example, a headband, includes elastic material, a low-friction sleeve, and a tube. The low-friction sleeve covers at least two opposing sides of a portion of the length of elastic material. The length of elastic material is affixed to the low-friction sleeve at a first end of the low-friction sleeve or a point adjacent to the first end of the low-friction sleeve. The length of elastic material extends beyond a second end of the low-friction sleeve opposite the first end of the low-friction sleeve. The tube substantially encloses the low-friction sleeve. The low-friction sleeve is affixed to the tube at the first end of the low-friction sleeve or a point adjacent to the first end of the low-friction sleeve, and the length of elastic material extends beyond a first end of the tube.

Abstract: An expandable joint for use in, for example, a headband, includes elastic material, a low-friction sleeve, and a tube. The low-friction sleeve covers at least two opposing sides of a portion of the length of elastic material. The length of elastic material is affixed to the low-friction sleeve at a first end of the low-friction sleeve or a point adjacent to the first end of the low-friction sleeve. The length of elastic material extends beyond a second end of the low-friction sleeve opposite the first end of the low-friction sleeve. The tube substantially encloses the low-friction sleeve. The low-friction sleeve is affixed to the tube at the first end of the low-friction sleeve or a point adjacent to the first end of the low-friction sleeve, and the length of elastic material extends beyond a first end of the tube.

Abstract: A jewelry apparatus including a power module, a magnetically permeable band connected to the power module, the magnetically permeable band including a core and a primary winding disposed around the core, the primary winding electrically connected to the power module. A bead can have an aperture shaped to receive the magnetically permeable band, the bead including a secondary winding positioned around the magnetically permeable band when the magnetically permeable band is received through the aperture, and at least one light source electrically connected to the secondary winding. The core in the magnetically permeable band can include a flexible band of magnetically permeable cores, or the core can otherwise be flexible. The jewelry apparatus can include a wireless transceiver either on the power module or the bead such that the jewelry apparatus can be communicated wirelessly with other jewelry apparatuses.

Abstract: A headband that includes a connecting material and a headband body connected to each other at their respective opposing ends. The headband body has an inner and outer edge, which may be curved. The distance between the inner and outer edge generally becomes shorter nearer the ends of the headband body. If curved, the inner and outer edges may have different radii, such that the tube is generally crescent shaped. The general crescent shape creates a more comfortable fit and results from the ratio of the radius of the inner edge curve to the radius of the outer edge curve being greater than about 1 and less than about 6. A more comfortable fit can also result from a particular ratio wherein the width at the center of the headband body is greater than the width at the ends of the headband body.