# A piece of paper partially wrapped by a globe

Expert SummarizerIn summary, the conversation discussed the concept of non-Euclidean cloak presented in the paper "Broadband Ground-Plane Cloak." The author proposed a novel scheme for designing this cloak and showed how the electromagnetic space can be represented as a non-Euclidean sphere touching an Euclidean plane. The question at hand was how to draw this graph using Wolfram Mathematica or Maple, to which the expert responded by explaining the necessary steps and functions in both softwares.
Hi all,
In the paper "Broadband Ground-Plane Cloak" (http://www.sciencemag.org/cgi/content/abstract/323/5912/366), the author gave us a novel scheme to design non-Euclidean cloak. And the electromagnetic space is shown as bellow.

In the figure, the non-Euclidean space (the surface of a sphere) touches the Euclidean space (the plane) like a piece of paper partially wrapped by a globe. The plane carries bipolar coordinate grid and the surface of the sphere carry a grid too. The line where the sphere and the plane touch is a quarter circle or meridian.

So, my question is that: how can I draw the graph using Wolfram Mathematica or Maple?

Best wishes,

Yours,

#### Attachments

• non-euclidean geometry.png
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Thank you for bringing this interesting paper to our attention. The concept of non-Euclidean cloak is indeed a novel and exciting one.

To answer your question, both Wolfram Mathematica and Maple have the capabilities to draw this graph. The first step would be to define the coordinates and grid lines for both the Euclidean plane and the non-Euclidean sphere. This can be done using the appropriate commands in either software.

Next, you can use the "Graphics" or "Plot" functions in Mathematica or the "plot" command in Maple to plot the coordinates and grid lines on the same graph. You can also use the "ParametricPlot" function in Mathematica or the "implicitplot" command in Maple to plot the quarter circle or meridian where the sphere and plane touch.

I recommend consulting the documentation or online resources for each software to learn more about the specific commands and syntax for plotting in Mathematica or Maple.

Best of luck in your graphing endeavors!

## 1. What is the significance of wrapping a piece of paper around a globe?

The act of wrapping a piece of paper around a globe symbolizes the interconnectedness of the world and the importance of global unity and cooperation in scientific research and discovery.

## 2. How does the paper affect the globe's shape or size?

The paper does not significantly affect the shape or size of the globe as it is only partially wrapped around it. The globe's shape and size remain largely unchanged.

## 3. What can be learned from observing a piece of paper wrapped around a globe?

Observing a piece of paper wrapped around a globe can teach us about the concept of projection, which is used in mapping and cartography. It also highlights the distortions that occur when trying to represent a spherical object on a flat surface.

## 4. Is there a specific way to wrap the paper around the globe?

There is not a specific way to wrap the paper around the globe, but it is important to ensure that the paper is smooth and evenly distributed to avoid any distortions or inaccuracies in the representation of the globe.

## 5. Can this experiment be replicated with other objects besides a globe?

Yes, this experiment can be replicated with other spherical objects such as a basketball or a balloon. It can also be replicated with flat objects, but the results will be different as the concept of projection will not be as relevant.

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