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Although the Greeks thought some constructions impossible all of the so called impossible problems were later proven to be possible in the 18th and 19th centuries?
This statement is false. Although the Greeks thought some constructions impossible, not all of the so called impossible problems were later proven to be possible.
Although the Greeks thought some constructions impossible all of the so-called impossible problems were later proven to be possible in the 18th and 19th centuries?
No. They were not proven to be possible.
What constructions were never accomplished by the Greeks with only a straightedge and a compass?
doubling a cube and trisecting any angle
Many of the same constructions the Greeks performed only with straightedge and compass can be done using only a straightedge and tracing paper?
True
What poople were credited with the systemization of geometry?
the Greeks
Although the Greeks thought some constructions impossible all of the so called impossible problems were later proven to be possible in the 18th and 19th centuries?
This statement is false. Although the Greeks thought some constructions impossible, not all of the so called impossible problems were later proven to be possible.
Although the Greeks thought some constructions impossible all of the so-called impossible problems were later proven to be possible in the 18th and 19th centuries?
No. They were not proven to be possible.
The ancient Greeks were ultimately able to prove that the constructions they thought impossible were impossible?
False
What did the Greeks use in geometric constructions?
A straightedge and compass.
What tools did the Greeks not use in geometric constructions?
Tracing paper, ruler.
Did the Greeks have no way of bisecting an angle because it is required a ruler in addition to a compass and straightedge?
The ancient Greeks were indeed limited in their geometric constructions to using only a compass and straightedge. While they developed methods for various constructions, angle bisection using just these tools is impossible for certain angles, such as a 60-degree angle, which leads to a 30-degree angle. This limitation is part of a broader set of problems in classical geometry that were proven to be impossible to solve with the restrictions they adhered to. Thus, the Greeks could not bisect all angles solely with a compass and straightedge.
What constructions were not accomplished by Greeks?
The Eiffel Tower, the Sydney Opera House, The Forbidden City, The Post office Tower, The Eddystone Light, The Taj Mahal, the Pantheon, The Empire state Building are just a few of the millions of constructions that were NOT accomplished by the Greeks.
Who invented constructions?
Greeks and Romans came up with it, I believe. A long, long time ago.
What ideas did the Greeks have for the cause of illness?
the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done the ancient Greeks thought that the gods were punishing them for bad things they have done
Which tools did the Greeks not use in their formal geometric constructions?
The ancient Greeks did not use measuring tools such as rulers or protractors in their formal geometric constructions. Instead, they relied on a compass for drawing circles and a straightedge for creating straight lines. Their constructions were based on pure geometric principles, emphasizing the use of these two simple tools to achieve precise results without any measurements.
What constructions were never accomplished by the Greeks with only a straightedge and a compass?
doubling a cube and trisecting any angle
Given only a compass and straightedge Greeks were able to construct only regular polygons and circles thus leaving many constructions impossible to complete.?
The Greeks, using only a compass and straightedge, could construct regular polygons and circles due to their ability to create precise geometric figures based on certain mathematical principles. However, some constructions, like trisecting an arbitrary angle or duplicating a cube, were proven impossible within these constraints, as they required the solution of cubic equations or other geometric constructs unattainable with just those tools. This limitation revealed the boundaries of classical geometric constructions and led to deeper explorations in mathematics. Ultimately, these challenges contributed to the development of modern algebra and geometry.
