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marciokoko
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Is there a way to determine the arc around 1/4 of the Earth without measuring it? I mean like thru trig?
It depends on what you mean by "determine". FYI, trig also involves measurements.marciokoko said:Is there a way to determine the arc around 1/4 of the Earth without measuring it? I mean like thru trig?
Ok today I was swimming and I have an app that records my swim sessions, SwimFit. I can tally up the number of meters I have covered since I started swimming and I was wondering how far across the world that would be.SteamKing said:It depends on what you mean by "determine". FYI, trig also involves measurements.
marciokoko said:Ok today I was swimming and I have an app that records my swim sessions, SwimFit. I can tally up the number of meters I have covered since I started swimming and I was wondering how far across the world that would be.
So while in the pool I had no access to data. And I was wondering what I could do to "guess-timate" the distance of 1/4 the circumference of the Earth in order to compare it to the meters I have swum since I started swimming.
anorlunda said:Just memorize one key approximate fact. The circumference of the Earth is about 25000 statue miles.
Or "statute" miles. Let's leave statues out of this.anorlunda said:Just memorize one key approximate fact. The circumference of the Earth is about 25000 statue miles.
Your definition of the meter (and the circumference of the earth, incidentally) is a tad off. 10,000 m is only about 6 statute miles.nasu said:Forget the miles. The meter was once defined so that one quarter of the circumference will be exactly 10,000 m.
The definition have changed several times since then but the meter itself did not change much.
1/4 Earth Arc is the distance along 1/4th of the circumference of the Earth's surface.
Trigonometry is used because it is the branch of mathematics that deals with the relationships between the sides and angles of triangles. Since the Earth's arc is a curved line, it can be broken down into smaller triangles, and trigonometry can be used to calculate the length of these segments.
The steps for calculating 1/4 Earth Arc with Trigonometry are as follows:
1. Determine the radius of the Earth (R).
2. Convert the given angle (θ) to radians.
3. Use the formula 1/4 Earth Arc = (θ/2π) * 2πR to calculate the length of 1/4 Earth Arc.
The units for 1/4 Earth Arc depend on the units used for the radius of the Earth (R) and the angle (θ). If the radius is given in kilometers and the angle is in radians, then the units for 1/4 Earth Arc will be kilometers. If the radius is given in miles and the angle is in degrees, then the units for 1/4 Earth Arc will be miles.
The accuracy of the calculation of 1/4 Earth Arc with Trigonometry depends on the accuracy of the given radius of the Earth (R) and angle (θ). If these values are accurate, then the calculation will be accurate. However, it is important to note that the Earth is not a perfect sphere, so there may be slight variations in the calculated value compared to the actual value.