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Toddler home math environment: Triangulating multi-method assessments in a U.S. Sample

Introduction Current research has documented the home math environment (HME) of preschoolers and kindergarteners. Very few studies, however, have explored the number and spatial activities in which parents engage with children during their toddler years. Methods This study examined the HME of 157 toddlers using several methodologies, including surveys, time diaries, and observations of math talk. Further, it examined correlations within and across data sources to identify areas of convergence and triangulation, and correlated HME measures with measures of toddlers’ number and spatial skills. Results Findings showed that, in general, uses of different types of math activities, including both number and spatial, were intercorrelated within method. Across methods, there was high intercorrelation between the frequency of math activities reported on parent surveys and the diversity of types of math activities endorsed in time diary interviews. Parent math talk gleaned from semi-structured interviews functioned as a separate aspect of the HME; different types of math talk shared few intercorrelations with engagement in math activities as reported in either surveys or time diaries. Finally, several HME measures positively correlated with toddlers’ math skills. Discussion Given extant research demonstrating that both math activities and math talk predict children’s math skills, our results stress the need for multimethod studies that differentiate among these HME opportunities.

Miller, Portia↗

Triangulation of multistation camera data to locate a curved line in space

A method is described for finding the location of a curved line in space from local azimuth as a function of elevation data obtained at several observation sites. A least-squares criterion is used to insure the best fit to the data. The method is applicable to the triangulation of an object having no identifiable structural features, provided its width is very small compared with its length so as to approximate a line in space. The method was implemented with a digital computer program and was successfully applied to data obtained from photographs of a barium ion cloud which traced out the earth's magnetic field line at very high altitudes.

Fricke, C. L.↗

Analytical expressions for position error in triangulation solution of point in space for several station configurations

Analytical expressions are derived to first order for the rms position error in the triangulation solution of a point object in space for several ideal observation-station configurations. These expressions provide insights into the nature of the dependence of the rms position error on certain of the experimental parameters involved. The station geometries examined are: (1) the configuration of two arbitrarily located stations; (2) the symmetrical circular configuration of two or more stations with equal elevation angles; and (3) the circular configuration of more than two stations with equal elevation angles, when one of the stations is permitted to drift around the circle from its position of symmetry. The expressions for the rms position error are expressed as functions of the rms line-of-sight errors, the total number of stations of interest, and the elevation angles.

Long, S. A. T.↗

Effects of various experimental parameters on errors in triangulation solution of elongated object in space

The effects of various experimental parameters on the displacement errors in the triangulation solution of an elongated object in space due to pointing uncertainties in the lines of sight have been determined. These parameters were the number and location of observation stations, the object's location in latitude and longitude, and the spacing of the input data points on the azimuth-elevation image traces. The displacement errors due to uncertainties in the coordinates of a moving station have been determined as functions of the number and location of the stations. The effects of incorporating the input data from additional cameras at one of the stations were also investigated.

Long, S. A. T.↗

Earth parameters from global satellite triangulation and trilateration

Results obtained from 159-station global satellite triangulation and trilateration (including Baker-Nunn, BC-4, PC-1000 camera observations, SECOR, C-Band radar and EDM distance measurements) indicate differences in the semidiameter and orientation of the earth compared to results obtained from dynamic satellite solutions. Geoidal undulations obtained can be made consistent with dynamically determined ones at the expense of slight changes in the currently accepted parameters defining the gravity field of the level ellipsoid.

Mueller, I. I.↗

Satellite triangulation in Europe from WEST and ISAGEX data

Observational data that was acquired during the West European Satellite Triangulation (WEST) program and the International Satellite Geodesy Experiment (ISAGEX) campaign was obtained for the purpose of performing a geometric solution to improve the present values of coordinates of the European stations in the OSU WN14 solutions, adding some new stations and assessing the quality of the WN14 solution with the help of the additional data available. The status of the data as received, the preprocessing required and the preliminary tests carried out for the initial screening of the data are described. The adjustment computations carried out and the results of the adjustments are discussed.

Leick, A.↗

Sequential triangulation of orbital photography

The feasibility of structuring the satellite photogrammetric triangulation as an iterative Extended Kalman estimation algorithm is demonstrated. Comparative numerical results of the sequential against batch estimation algorithm are presented. Difficulty of accurately modeling of the attitude motion is overcome by utilizing the on-board angular rate measurements. Solutions of the differential equations and the evaluation of state transition matrix are carried out numerically.

Rajan, M.↗

A linear photodiode array employed in a short range laser triangulation obstacle avoidance sensor

An opto-electronic receiver incorporating a multi-element linear photodiode array as a component of a laser-triangulation rangefinder was developed as an obstacle avoidance sensor for a Martian roving vehicle. The detector can resolve the angle of laser return in 1.5 deg increments within a field of view of 30 deg and a range of five meters. A second receiver with a 1024 elements over 60 deg and a 3 meter range is also documented. Design criteria, circuit operation, schematics, experimental results and calibration procedures are discussed.

Odenthal, J. P.↗

Three dimensional mesh generation by triangulation of arbitrary point sets

A method for generating an unstructured mesh is described. The approach is quite general and joins an arbitrary set of points to produce a covering of three dimensional space by tetrahedra. After removing the tetrahedra that connect surface points, a mesh suitable for a finite element based flow solver is obtained. Details of the triangulation algorithm are provided together with an analysis of the algorithm efficiency and validity.

Baker, Timothy J.↗

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗

Advancing-Front Algorithm For Delaunay Triangulation

Efficient algorithm performs Delaunay triangulation to generate unstructured grids for use in computing two-dimensional flows. Once grid generated, one can optionally call upon additional subalgorithm that removes diagonal lines from quadrilateral cells nearly rectangular. Resulting approximately rectangular grid reduces cost per iteration of flow-computing algorithm.

Merriam, Marshal L.↗

Global positioning system reoccupation of early triangulation sites - Tectonic deformation of the Southern Coast Ranges

We study tectonic deformation in the Southern Coast Range, California. We use triangulation and astronomic azimuth data collected since 1875, trilateration since 1970, and global positioning system data collected from 1986 to 1987. Two modeling techniques have been used. An elastic block-fault model is applied to study the tectonic motion of the San Andreas Fault and the San Gregorio-Hosgri Fault. Station velocities are modeled to study regional deformations. Results show that the regional deformation is predominantly controlled by deep strike-slip motion along the San Andreas Fault, at a rate of 33 +/- 2 mm/yr. Deep slip along the San Gregorio-Hosgri Fault is about 0-4 mm/yr, assuming a locked suit to a depth of 20 km. Convergence normal to the San Andreas Fault in the Southern Coast Ranges is not greater than 0.02 microrad/yr.

Shen, Zheng-Kang↗