Answer to Question #350386 in Geometry for Amaret

Question

1.2. Measurement

(a) where in the world that people measured things?

(b) approximately 2 what year does this evidence date back?

(c) give details of how measuring was done in that time?

(d) where in the caps is this type of geometry covered as topic?

Answer 1

The earliest known uniform systems of weights and measures seem all to have been created at some time in the 4th and 3rd millennia BC among the ancient peoples

of Egypt, Mesopotamia and the Indus Valley, and perhaps also Elam (in Iran) as well.

Early Babylonian and Egyptian records and the Hebrew Bible indicate that length was first measured with the forearm, hand, or finger and that time was measured by the periods of the sun, moon, and other heavenly bodies. When it was necessary to compare the capacities of containers such as gourds or clay or metal vessels, they were filled with plant seeds which were then counted to measure the volumes. When means for weighing were invented, seeds and stones served as standards. For instance, the carat, still used as a unit for gems, was derived from the carob seed

The Egyptian cubit, the Indus Valley units of length referred to above and the Mesopotamian cubit were used in the 3rd millennium BC and are the earliest known units used

by ancient peoples to measure length. The units of length used in ancient India included the dhanus, or dhanush (bow), the krosa (cry, or cow-call) and the yojana (stage).

The common cubit was the length of the forearm from the elbow to the tip of the middle finger. It was divided into the span of the hand or the length between the tip of little finger to the tip of the thumb (one-half cubit), the palm or width of the hand (one sixth), and the digit or width of the middle finger (one twenty-fourth). The Royal Cubit, which was a standard cubit enhanced by an extra palm—thus 7 palms or 28 digits long—was used in constructing buildings and monuments and in surveying in ancient Egypt. The inch, foot, and yard evolved from these units through a complicated transformation not yet fully understood. Some believe they evolved from cubic measures; others believe they were simple

proportions or multiples of the cubit. In whichever case, the Greeks and Romans inherited the foot from the Egyptians. The Roman foot (~296 mm) was divided into both 12 unciae (inches) (~24.7 mm) and 16 digits (~18.5 mm). The Romans also introduced the mille passus (1000 paces) or double steps, the pace being equal to five Roman feet (~1480 mm). The Roman mile of 5000 feet (1480 m) was introduced into England during the occupation. Queen Elizabeth I (reigned from 1558 to 1603) changed, by statute, the mile to 5280 feet (~1609 m) or 8 furlongs, a furlong being 40 rod (unit)s (~201 m) of 5.5 yards (~5.03 m) each.

The grain was the earliest unit of mass and is the smallest unit in the apothecary, avoirdupois, Tower, and troy systems. The early unit was a grain of wheat or barleycorn used to weigh the precious metals silver and

gold. Larger units preserved in stone standards were developed that were used as both units of mass and of monetary currency. The pound was derived from the mina (unit) used by ancient civilizations. A smaller unit was the shekel, and a larger unit was the talent. The magnitude of these units varied from place to place. The Babylonians and Sumerians had a system in which there were 60 shekels in a mina and 60 minas in a talent. The Roman talent consisted of 100 libra (pound) which were smaller in magnitude than the mina. The troy pound (~373.2 g) used in England and the United States for monetary purposes, like the Roman pound, was divided into 12 ounces, but the Roman uncia (ounce) was smaller. The carat is a unit for measuring gemstones that had its origin in the carob seed, which later was standardized at 1/144 ounce and then 0.2 gram.

Topics of CAPS:

• Estimation in two- and three-dimensional figure measurement
• Area and volume
• Introduction to geometry
• Pythagorean theorem
• Trigonometric ratios and using trigonometry
• Transformation and symmetry
• Introduction to coordinates
• Coordinate geometry of straight lines
• Introduction to deductive geometry
• Congruence and similarity
• Angles related to lines and rectilinear figures
• Quadrilaterals