The {Mathematics|Arithmetic} of Origami

{If you have|When you have|In case you have|When you’ve got|If in case you have|You probably have} ever held {a piece|a bit|a chunk} of origami in your hand {you have|you’ve|you could have|you’ve got|you might have|you will have|you’ve gotten|you have got|you may have} {in all probability|most likely|perhaps|possibly} been {at least|a minimum of|no less than|at the least|at the very least|not less than} tempted to open it {just|simply} to see how the folding was done. The geometry {involved|concerned} {in the|within the} piece is {something|one thing} {you could|you can|you would|you may|you might|you possibly can|you could possibly} {easily|simply} see {in the|within the} creases displayed on the opened paper.

Scientists and artists have studied these geometric {aspects|elements|features|points|facets} {as well as|in addition to} origamists and mathematicians. Mathematicians {throughout|all through} time have developed {ways|methods} {to use|to make use of} geometry to {define|outline} origami; {they have|they’ve} designed {highly|extremely} {sophisticated|refined|subtle} {models|fashions} {using|utilizing} {fundamental|elementary|basic} theorems. {They have|They’ve} studied {and found|and located} {amazing|superb|wonderful} similarities between tessellations and origami (tessellations is the {name|identify|title} for a {figure|determine} comprised of a {shape|form} {that is|that’s} repeated {over and over again|again and again|time and again|over and over} with no gaps or overlap when fitted to a flat {surface|floor}). {Teachers|Academics|Lecturers} {around the world|around the globe|all over the world|world wide} have used origami {to teach|to show} {different|totally different|completely different} {concepts|ideas|ideas} in chemistry, physics and {architecture|structure} {as well as|in addition to} math.

Origami {construction|development|building} is {defined|outlined} {as the|because the} folding of paper {using|utilizing} the {raw|uncooked} edges, {points|factors} of the paper and any creases or {points|factors} subsequently created by {those|these} folds. The folded paper is seen as {both|each} an {art|artwork} piece and {a geometric|a geometrical} form. The folds produce {varying|various} sizes of triangles, rectangles and {other|different} shapes. A single fold can bisect and angle twice or as {in the|within the} case of a reverse fold, make {4|four} triangles at once.

When {the first|the primary} steps {to making|to creating} a {figure|determine} are {applied|utilized} to {other|different} figures, {resulting in|leading to} {a number of|numerous|a variety of|quite a few|various|quite a lot of|a lot of|plenty of} figures having {common|widespread|frequent} shapes, the {common|widespread|frequent} shapes are {called|referred to as|known as} bases. There are {several|a number of} established bases such {as the|because the} {bird|chook|fowl|hen|chicken}, the kite, the windmill and the water-bomb {to name|to call} a few. {Modern|Trendy|Fashionable} origami {relies|depends} {heavily|closely} on these {existing|present|current} bases alone and {in combination|together} when designing new figures. {As an example|For instance|For example} the kite base is used to make {quite|fairly} {a few|a couple of|a number of|just a few} of the {different|totally different|completely different} zoo animals. {Studying|Learning|Finding out} the creases of {existing|present|current} {models|fashions} has led to the creation of many new models. These creases {show|present} {definite|particular} patterns of triangles, rectangles and {other|different} shapes. The geometric {study|research|examine} of the crease {lines|strains|traces} {over the last|during the last|over the past} twenty-{five|5} years has paved {the way|the best way|the way in which} for {the discovery|the invention} {of new|of latest|of recent} bases. Not all designs are {combinations|mixtures|combos} or {parts|elements|components} of {other|different} bases; some {like the|just like the} {box|field} pleat are {completely|utterly|fully} original.

Some origamists {saw|noticed} {the base|the bottom} as a set of areas {each|every} {independent|unbiased|impartial} of {the other|the opposite} differing {only|solely} {in their|of their} {length|size} and arrangement. With this in {mind|thoughts} they went on to develop {computer|pc|laptop} {programs|packages|applications} {that are|which are|which might be|which can be} {capable of|able to} doing all {the math|the maths|the mathematics} {necessary to|essential to} generate crease patterns for any base from a given {length|size} and {area|space} arrangement. With {the aid of|assistance from|the help of} {computer|pc|laptop} {programs|packages|applications} {using|utilizing} intricate mathematical theorems origami has {become|turn out to be|turn into|develop into|grow to be|change into} as {much|a lot} a puzzle as {a piece|a bit|a chunk} of art. Mathematical origamists {are now|at the moment are|are actually} designing {more and more|increasingly more|increasingly|an increasing number of} {complex|complicated|advanced}, {realistic|practical|sensible|reasonable|real looking|lifelike|life like} {models|fashions} {still|nonetheless} sticking to {the simple|the straightforward|the easy} rule {of one|of 1} sheet of paper with no cuts. These {programs|packages|applications} are {also|additionally} used {to solve|to unravel|to resolve} {problems|issues} involving getting {large|giant|massive} {pieces|items} of paper folded {to fit|to suit} {a specific|a selected|a particular} sized flat surface.