# What is the name of a shape with an infinite perimeter?

Table of Contents

- 1 What is the name of a shape with an infinite perimeter?
- 2 What is a shape defined by a mathematical equation that has infinite surface area but finite volume?
- 3 Why is Gabriel’s horn a paradox?
- 4 How can an infinite perimeter enclose a finite area?
- 5 How can an object with finite area have infinite perimeter?
- 6 What is Gabriel’s cake?
- 7 How do you make a space filling curve in Revit?
- 8 When is a space a continuous image of the unit interval?

## What is the name of a shape with an infinite perimeter?

Koch snowflake

A shape that has an infinite perimeter but finite area.

## What is a shape defined by a mathematical equation that has infinite surface area but finite volume?

Gabriel’s horn (also called Torricelli’s trumpet) is a particular geometric figure that has infinite surface area but finite volume.

**What’s the infinite shape?**

A fractal is any shape that has infinite self-symmetry, meaning if you zoom in forever, you’ll get a repeating pattern.

### Why is Gabriel’s horn a paradox?

It is the Painter’s Paradox given below: The inner surface of the Gabriel’s horn is infinite; therefore an infinite amount of paint is needed to paint the inner surface. But the volume of the horn is finite ( \pi ), so the inner surface can be painted by pouring a \pi amount of paint into the horn and then emptying it.

### How can an infinite perimeter enclose a finite area?

has infinite length between x = 0 and any other point, say P. So if you draw a connecting line between P and the origin which does not cross or touch the curve, you have a shape with infinite perimeter enclosing a finite area.

**How does Gabriel’s Horn have infinite surface area?**

But this implies that the surface area of Gabriel’s Horn is infinite! 2π (1 x )√ 1 + [ – 1 x2 ]2 dx = с. So we have a surface with infinite surface area enclosing a finite volume. In essence, we have a “bucket” that would take an infinite amount of material to make, but which holds a finite amount of stuff.

## How can an object with finite area have infinite perimeter?

The areas enclosed by the successive stages in the construction of the snowflake converge to 85 times the area of the original triangle, while the perimeters of the successive stages increase without bound. Consequently, the snowflake encloses a finite area, but has an infinite perimeter.

## What is Gabriel’s cake?

Thus, this solid illustrates essentially the same paradox as Gabriel’s horn: an infinite solid with finite volume and infinite surface area. In other words: a cake you can eat, but cannot frost. Regarding a name for this new solid, Gabriel’s wedding cake seems appropriate for physical and genelogical reasons.

**Is there a non-self-intersecting space-filling curve?**

There exist non-self-intersecting curves of nonzero area, the Osgood curves, but they are not space-filling. For the classic Peano and Hilbert space-filling curves, where two subcurves intersect (in the technical sense), there is self-contact without self-crossing.

### How do you make a space filling curve in Revit?

To create a space-filling curve from a rep-tile, start by subdividing it into copies of itself and connecting the centers of those copies with lines to create the first-iteration curve. Replace each subdivision with the first iteration and connect the copies to create the second iteration.

### When is a space a continuous image of the unit interval?

A non-empty Hausdorff topological space is a continuous image of the unit interval if and only if it is a compact, connected, locally connected, second-countable space. Spaces that are the continuous image of a unit interval are sometimes called Peano spaces .

**What is the limit of the Peano curve?**

Three iterations of the Peano curve construction, whose limit is a space-filling curve. In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an n -dimensional unit hypercube ).