page_title: Catenary
hierarchical_section_title: Catenary
caption_attribution_description: Kette Kettenkurve Catenary
context_page_description: A catenary is a type of curve. An ideal chain hanging between two supports and acted on by a uniform gravitational force makes the shape of a catenary. The supports can be at different heights and the shape will still be a catenary. A catenary looks a bit like a parabola, but they are different.
  The equation for a catenary in Cartesian coordinates is
  where is a parameter that determines the shape of the catenary and cosh is the hyperbolic cosine function, which is defined as
  .
  Hence, we can also write the catenary equation as
  .
  The word "catenary" comes from the Latin word catena, which means "chain". A catenary is also called called an alysoid and a chainette.
context_section_description: A catenary is a type of curve. An ideal chain hanging between two supports and acted on by a uniform gravitational force makes the shape of a catenary. (An ideal chain is one that can bend perfectly, cannot be stretched and has the same density throughout.) The supports can be at different heights and the shape will still be a catenary. A catenary looks a bit like a parabola, but they are different.
  The equation for a catenary in Cartesian coordinates is
  where  is a parameter that determines the shape of the catenary and cosh is the hyperbolic cosine function, which is defined as
  .
  Hence, we can also write the catenary equation as
  .
  The word "catenary" comes from the Latin word catena, which means "chain". A catenary is also called called an alysoid and a chainette.
caption: A chain hanging like this forms the shape of a catenary approximately
exif: {"Image ImageDescription": "OLYMPUS DIGITAL CAMERA", "Image Make": "OLYMPUS IMAGING CORP.", "Image Model": "FE100,X710", "Image Orientation": "Horizontal (normal)", "Image XResolution": "314", "Image YResolution": "314", "Image ResolutionUnit": "Pixels/Inch", "Image Software": "1.2", "Image DateTime": "2008:08:11 17:42:02", "Image YCbCrPositioning": "Co-sited", "Image ExifOffset": "840", "Image PrintIM": "[80, 114, 105, 110, 116, 73, 77, 0, 48, 51, 48, 48, 0, 0, 37, 0, 1, 0, 20, 0, ... ]", "Thumbnail Compression": "JPEG (old-style)", "Thumbnail XResolution": "72", "Thumbnail YResolution": "72", "Thumbnail ResolutionUnit": "Pixels/Inch", "Thumbnail JPEGInterchangeFormat": "3556", "Thumbnail JPEGInterchangeFormatLength": "4705", "EXIF ExposureTime": "1/200", "EXIF FNumber": "17/5", "EXIF ExposureProgram": "Program Normal", "EXIF ISOSpeedRatings": "64", "EXIF ExifVersion": "0221", "EXIF DateTimeOriginal": "2008:08:11 17:42:02", "EXIF DateTimeDigitized": "2008:08:11 17:42:02", "EXIF ComponentsConfiguration": "YCbCr", "EXIF ExposureBiasValue": "1", "EXIF MaxApertureValue": "317/100", "EXIF MeteringMode": "CenterWeightedAverage", "EXIF LightSource": "Unknown", "EXIF Flash": "Flash did not fire, compulsory flash mode", "EXIF FocalLength": "42/5", "EXIF FlashPixVersion": "0100", "EXIF ColorSpace": "sRGB", "EXIF ExifImageWidth": "2272", "EXIF ExifImageLength": "1704", "Interoperability InteroperabilityIndex": "R98", "Interoperability InteroperabilityVersion": "[48, 49, 48, 48]", "EXIF InteroperabilityOffset": "3432", "EXIF FileSource": "Digital Camera", "EXIF CustomRendered": "Normal", "EXIF ExposureMode": "Manual Exposure", "EXIF WhiteBalance": "Auto", "EXIF DigitalZoomRatio": "1", "EXIF SceneCaptureType": "Standard", "EXIF GainControl": "None", "EXIF Contrast": "Normal", "EXIF Saturation": "Normal", "EXIF Sharpness": "Normal"}