Seven Images
I will be organizing my website into 4 tabs: a general overview of the theorem, background information (including topics in differential geometry and topology), the theorem itself along with is proof, direct applications of it.
.jpg)
Image 01
Curves
This photo will be in the general overview tab when introducing the concept of curves. I blended two images of curves to create the image here to the left.
Image 02
Surfaces
Arguably the most important surface in 3D space is the sphere. Here, I have edited a photo of a bubble, adding the photo daubs filter onto it.
.jpg)
.jpg)
Image 03
Gravitational Lensing
One of the applications of Gauss Bonnet is on gravitational lensing. Here, I blended an image of the universe over an image of a camera lens using the linear burn option.
Image 04
Topology
This image will be used when introducing topics in topology. The study of topology is basically the study of manifolds, the most popular of which is the torus; a donut shape! Here, I collected an image of 6 donuts, enhanced it, blended an image of crumpled paper over it to give it texture, added text, and then added texture to the text in the same way.
.jpg)
%20(1).jpg)
Image 05
Website Title
Here is an example of a title image. I took an image of a hand using a sharpie, used the "lighten" blend option to overlay an image of math equations, and created a masked text that states the title of the theorem.
Image 06
Gauss Quote
Since I am studying the Gauss-Bonnet Theorem, I thought it would be a good idea to include a quote from Carl Gauss. I began with an image of a royal hallway, blended a picture of the royal cards, overlaid this with a blend of mathematical equations, and included my quote on an image of a ripped piece of paper.
.jpg)
.jpg)
Image 07
Collage
The Gauss Bonnet Theorem links the world of topology with the world of differential geometry. I tried to represent this here by showing the main topics of differential geometry, surfaces and curves, by choosing an image of nature showcasing curves and using the quick selection tool on four images of planets and the moon so they stood alone to represent examples of a spherical surface. I then used the quick selection tool again to place 4 images of ripped paper on the top right and bottom left corner, including elements of topology here, which says that all of the images included (a torus, a donut, a lifesaver, and a mug) are the same.