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we as humans are curious creatures and we discovered a lot of things because of that one of them being geometry which a lot of the credit for it go to the Egyptians and there want to know surface areas and volume. soon geometry would evolve into what we see today now let me show you how that happened.

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This is Euclid he is often referred to as the father of Geometry. He discovered Geometry in the year 300 BC

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This is Archimedes he is often referred as the founder of math even though he came after Euclid. he discovered the surface and volume of a sphere and its circumscribing cylinder.

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The Sumerians where the first known civilization with math back in 3000 BC. The Sumerians developed a numerical system based on the sexagesimal system (base 60), which is still in use for measuring time (seconds, minutes, and degrees in a circle) today.

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The earliest recorded beginnings of geometry can be traced to early peoples, such as the ancient Indus Valley and ancient Babylonia from around 3000 BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.

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Analytic Geometry was first used by the French mathematician who introduced Rene Descartes who introduced rectangular coordinates to locate points and to enable lines and curves to be represented with algebraic equations.

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In several ancient civilizations a for was developed to determine the relationship between lengths, area, and volumes of a physical object which would become known as Euclidean geometry.

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Projective geometry originated from a French mathematician named Girard Desargues to deal with those properties of geometric figures that are not altered by shadows onto another object or projection of their image.

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The German mathematician Carl Friedrich Gauss (1777–1855), in connection with practical problems of surveying and geodesy, initiated the field of differential geometry. Using differential calculus, he characterized the intrinsic properties of curves and surfaces. For instance, he showed that the intrinsic curvature of a Cylinder is the same as that of a plane, as can be seen by cutting a cylinder along its axis and flattening, but not the same as that of a sphere, which cannot be flattened without distortion.

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Beginning in the 19th century, various mathematicians substituted alternatives to Euclid’s parallel postulate, which, in its modern form, reads, “given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line.” They hoped to show that the alternatives were logically impossible. Instead, they discovered that consistent non-Euclidean geometries exist.

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Topology, the youngest and most sophisticated branch of geometry, focuses on the properties of geometric objects that remain unchanged upon continuous deformation—shrinking, stretching, and folding, but not tearing.

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The earliest known examples of written records—dating from Egypt and Mesopotamia about 3100 BCE—demonstrate that ancient people had already begun to devise mathematical rules and techniques useful for surveying land areas, constructing buildings, and measuring storage containers.

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Back before we had a level. trying to make sure we got a perfect right angle was really hard to do. so ancient Egyptians used ropes to find the right angle and this worked until they created the this worked by marking a rope with knots and when held on those knots and pulled tight they would Form a right angle.

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The ancient Chinese arrived at measures of inaccessible heights and distances by using another method, using “complementary” rectangles, as seen in the photo, which can be shown to give results equivalent to those of the Greek method involving triangles.

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with each advancement in geometry we made a new geometric shape or object like its geometric writing and we may still have more to discover and we may have more shapes to discover or different forms of the shapes we have already discovered

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he was the first person to think that even the most obvious of things still needed proof such as an isosceles triangles opposite sides being equal. this is still used today and it has its purposes and helps with many other things than just math.

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1. we are given that angle ABC is an isosceles triangle-that is, that AB=AC.

2. extended sides AB and AC indefinitely away from A.

3. With a compass centered on A and open to a distance larger than AB mark off AD on AB extended and AE on AC extended so that AD=AE.

4. Angle DAC=angle EAB, because it is the same angle.

5. Therefore. triangle DAC is congruent to triangle EAB; that is, all the corresponding sides and angles of the 2 triangles are equal. by imagining one triangle to be superimposed on another, Euclid argued that the 2 are congruent if 2 sides and the included angle of one triangle are equal to the corresponding 2 sides and included angle of the other triangle (known as the SAS theorem).

6. Therefore, angle ADC=angle AEB and DC=EB by step 5.

7. Now BD=CE because BD=AD-AB, CE=AE-AC,AB=AC,and AD=AE, all by construction.

8. triangle BDC is congruent to triangle CEB, by the SAS theorem of step 5.

9. Therefore, angle DBC=angle ECB, by step 8.

10. Hence, angle ABC=angle ACB because angle ABC=180 degrees-angle DBC and angle ACB=180 degrees-angle ECB.

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It is the statement that if A squared + B squared = C squared only in right triangles.

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An object that expands endlessly in a 2 dimensional plane created by two number lines.

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Two parallel lines that never cross get intercepted by another line called the transversal creating angles.