Proving the Kawasaki Theorem

Then turn your right hand counter clockwise. Extend the left index finger, and hook the section of the hair between the right index and middle fingers. Pull it to the left, and let the section in your right hand hang down.

They say in easy enough steps to "cross the longer end over the shorter end, loop the long end under where the two ends cross, fold the dangling end to make a loop, drop the longer end over the center, pinch the bow together in front of the long end, and feed the middle of the dangling end back through the knot." (wikihow 7). Now I don't know about you but that is just a lot of words to follow. Thankfully the webiste had pictures for this process and were easy enought to navigate with the instructions listed beneath them.

Cut a kerf on one edge of a stile or rail. Rotate the part end-for-end and make the second pass to complete the groove. Repeat both cuts for the remaining rails and stiles.

Now you should have two pieces of paper that look the same. You want to fold both the pieces in half so you make a crease in the middle. Now you want to take one of your pieces and fold the top right edge down to the middle crease you just made. Then turn it around and once again fold the top edge down to the middle crease. Next take the other half, but this time fold the bottom edge up to the middle crease. Then turn it around and fold the other bottom edge up to the middle crease again. Now you should have to pieces that look like this, where both are going opposite ways. Now you want to take the long ends from each piece and fold them to the middle edge, like this. Then do the same on the other piece. You should now have a square shape on the top and bottom of each piece. Next you take the top outside corner and fold it down to opposite corner, like this. You want to repeat this step for both squares on each piece. Now the pieces should look like a ‘s’ and ‘z’ shape. Now you

the following pits in sequence and putting your stones into your base on the end of board. This

I will start with the first question. I think origami has not affected me yet. When I folded origami designs, it did not change, help, or affect me. I have done it a few times last year with my friend because she had a book about it, but I just made a few designs, I was not very good at it, and I didn’t really think about it other than entertainment.

Lay your shirt face down on the folder vertically with the neck to the top. Fold the right two panels to the center. Leave the shirt, but pull the panels back. Repeat this move on the left. Fold the panel in the center bottom up toward the top. You now have a perfectly folded

From there, five more cuts will be made, all being mitre cuts of 45 degrees, but in different directions. Cut the end of the wood 45 degrees from the corner of the wood for the very first cut. From here, a 125 degree cut at 10” from the base of the wood can be made to complete the very first piece of the frame. From here, another 45 degree cut can be made at 6 ½” along the bottom of the wood to complete the second piece, 125 degree cut 8” from the bottom of the wood for the third piece, 45 degree cut 4 ½” from the bottom of the wood, and finally another 125 degree angle cut at the end of the wood to complete the fourth and final piece. This should result in four equal sized pieces that will be fastened in the future. Doing these cuts in a zigzag fashion utilizes as much wood as

Next, fold the top corners towards the middle. Make sure that the edges meet to form two triangles.

Trailing edge folds are not without downsides be that as it may. Chief among these is a huge increment in drag when they are utilized. Because of the sharp, discrete way in which they change the airfoils camber, sudden changes in weight and stream detachment are average, bringing about expansive increments in drag over the standard airfoil, especially everywhere lift coefficients. Numerous analysts and creators have looked to address this deficiency by utilizing "transforming" structures to make a smooth and constant change in camber along

The shape of an airplane's wings is what makes it able to fly. Airplanes' wings are curved on top and flatter on the bottom. That shape makes air flow over the top faster than under the bottom. So, less air pressure is on top of the wing. This condition makes the wing, and the airplane it's attached to, move up. Using curves to change air pressure is a trick used on many aircraft. Helicopter rotor blades use this trick. Lift for kites also comes from a curved shape. Even sailboats use this concept. A boat's sail is like a wing. That's what makes the sailboat move.

Bowing - Bowing is created when the cross-grain weft bends additionally down the table in the center of the goods only. This condition is difficult to minimize, so in extreme cases, the fabric will be rejected.

This mathematics exploration gives me the opportunity for me to explore the various aspects on how mathematics can be used in real life situations. Since I had the specific interest of origami, I wanted to apply and test the mathematical principles in origami. I have also discovered that geometrical principles and patterns exist in the folding of paper and in the basic rules of origami. The theories such as Maekowa's theorem exist in the folding of paper in origami.

The with Planform area in the shape of a Triangle is called a Delta wing.

A great advantage of folding is how it creates structural stiffness with geometry. When we add folds onto a planar material, it gains toughness and rigidity. Strategically placed folds enable the material to potentially span longer distances, the folds also often turn the