Is There a Solution to the Inconvenient Expression for Area and Element of Area?

In summary, the conversation discusses the inconvenience of the equation dA = dx dy and the desire for a more convenient expression where A = x y and dA = dx dy. The issue of defining this problem is also brought up.
  • #1
Bruno Tolentino
97
0
If A = x y (if the area of the paralelepid A is equal to edge x multiplied by edge y), so, dA is equal dx y + x dy. See:

But this is so much incovenient! The convenient would be dA = dx dy.

Let's see now d²A...

d²A = d dA = d²x y + dx dy + dx dy + x d²y

Now dx dy appears! But, is not a convenient expression, because d²x y and x d²y appears too in the equation!

How to solve this problem? We want that A = x y and dA = dx dy. Do you understand this conceptual problem of defition?
 
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  • #2
It would also be very convenient that every number is rational.
 
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What is the difference between area and element of area?

The area refers to the measure of the extent of a two-dimensional surface or shape, while the element of area is a small part or unit of the overall area. In other words, the element of area is a small portion of the total area.

How is area calculated?

The area of a two-dimensional shape can be calculated by multiplying the length and width of the shape. For more complex shapes, such as circles or triangles, there are specific formulas that can be used to calculate the area.

What is the unit of measurement for area?

The unit of measurement for area is typically square units, such as square inches, square feet, or square meters. These units represent the amount of space that is enclosed within a shape.

Why is understanding area important in science?

Understanding the concept of area is important in science because it allows us to measure and compare the sizes of different two-dimensional objects. This is crucial in many scientific fields, such as physics, engineering, and geography.

How does the concept of area relate to real-world applications?

The concept of area has many real-world applications, such as determining the amount of material needed to cover a surface, calculating the size of a plot of land, or finding the surface area of an object. It is also used in everyday tasks, such as measuring the size of a room or determining the amount of paint needed to cover a wall.

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