Tag Archives: Area

Area from Vectors

The previous post looked at User Defined Functions (UDFs) for working with vectors, including examples of functions to find the area of polygons defined by coordinates.  In this post the functions will be extended to find other section properties (such … Continue reading

Posted in Arrays, Coordinate Geometry, Excel, Maths, UDFs, VBA | Tagged , , , , , , | 5 Comments

Section Properties from Coordinates Without VBA

At the Eng-Tips forum there was a question asking for a calculation of area and centroid values from coordinates without the use of VBA.  In my opinion using VBA is much the easiest and most robust way to do it, … Continue reading

Posted in Coordinate Geometry, Excel, Newton, UDFs, VBA | Tagged , , , , , | 13 Comments

Cubic Spline Update

The previous post in this series presented a User Defined Function (UDF) to fit  a cubic spline to a series of points defined by XY coordinates.  Each segment of the resulting spline is defined by a separate cubic curve, which may be … Continue reading

Posted in Coordinate Geometry, Excel, Maths, Newton, UDFs, VBA | Tagged , , , , | 1 Comment

Elegant proofs 2 – The area of a circle

We are so familiar with the formula for the area enclosed by a circle that we tend not to think much about how it was derived, at least I don’t. The proofs of the formula are in fact many and … Continue reading

Posted in Maths, Newton | Tagged , , , , | 4 Comments

Section Properties from Layers

An alternative to finding the section properties of irregular polygons from the coordinates of the corners is to divide the shape into rectangular or trapezoidal layers.  The properties of the shape may then be found by simply summing the properties … Continue reading

Posted in Maths, Newton, Uncategorized | Tagged , , , , | 1 Comment

Section Properties from Coordinates

The area of irregular closed polygons defined by coordinates may be conveniently calculated by summing the areas of adjacent trapeziums, as shown below.   The area of each trapezium is calculated from the X axis.  Note that with the apex coordinates … Continue reading

Posted in Maths, Newton | Tagged , , , , | 2 Comments