What Is a Delta Shape in Mathematics? 

Delta is a common symbol used in maths and science. It is a Greek letter and can be interpreted to represent a variety of different concepts. For example, it can mean “change” or “the change,” or a variation on that theme. It can also be a measure of infinitesimal changes in one variable, and is often used to represent a derivative. 

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A delta is a type of landform formed by the mouth of a river as it empties into an ocean or lake. They occur in many places worldwide, but not every river forms a delta. 

In order to create a delta, a river must deposit sediment into the ocean. Then, the waves of the ocean rework that sediment. The reworked sediments are pushed back along the coastline, forming the delta. 

The reworking process can be smooth and relatively uniform, or it can fan out in a more pointed shape. In the latter case, it is called a cuspate delta, or a tooth-shaped delta. A delta can also be triangle-shaped, with its tributaries forming narrow, widely spaced islands that resemble the wings of a bird. 

There are two main types of deltas, based on their influence on the sediment deposition: river-dominated and wave-dominated. In a wave-dominated delta, the river’s force is not strong enough to push the sediment, so the coastline is relatively smooth and flat. This type of delta can be seen at the mouths of rivers that empty into the Mediterranean Sea, like the Nile River, and on the coast of Brazil. 

River-dominated deltas form when the river’s force is much stronger than ocean waves. These deltas, such as the Nile River, can be triangular-shaped or a little more rounded, with a narrower sand bar and a smaller distribution of distributaries than a wave-dominated delta. 

Tides are another factor that limits the formation of deltas. If the tides are too strong, the deposited sediment will be swept away as soon as it is deposited in the water. In addition, strong ocean waves can cause a river to break up into several tributaries and channels, rather than forming a single delta. 

The new MIT-WHOI method can predict the reworking of a delta’s coastline in a relatively simple way, given two factors: the strength of the river’s force and the strength of the ocean waves. In some cases, this can help scientists estimate how a delta will evolve with climate change, as ocean waves may become more powerful and more intense over time. 

This metric can also be useful for engineers if they need to understand how the Mississippi’s shape will shift if they erect dams or levees along its banks. That’s because the river’s flow may be altered by a dam or levee, and its sediment may be shifted along the coast. 

The MIT-WHOI team tested the new delta shape metric on 25 river deltas in Java, a region where sediments have deposited over a shallow continental shelf. For each delta, they measured the force of incoming ocean waves and a river’s sediment flux to the ocean. They then compared the results with satellite images to identify a delta’s shape.