A ring binder for holding punched paper is configured using two or more curved rotational ring elements (CREs) and corresponding post elements. A linkage mechanism couples the CREs together so that the rotate in unison. When a CRE engages a corresponding post element a ring element is formed for holding punched paper. The interface between the CRE and the post element has features that ensure that the interfaces have minimum gapping and they resist separation in a direction perpendicular to the tangent to the arc of rotation when the rings are closed. The linkage may be latched against rotation. Likewise the interfaces between the CREs and the post elements may be detented to ensure minimum gapping. The mechanism may have features that break the detent before rotation commences. Ring binders with two or more rings may be formed in a variety of sizes.