Fractions - Decimal Calculator. Egyptian Fractions. 1 Egyptian Fractions The ancient Egyptians only used fractions of the form 1/n so any other fraction had to be represented as a sum of such unit fractions and, furthermore, all the unit fractions were different!
Why? Is this a better system than our present day one? In fact, it is for some tasks. This page explores some of the history and methods with puzzles and and gives you a summary of computer searches for such representations. This page has an auto-generated Content section which may take a second or two to appear. The calculators on this page also require JavaScript but you appear to have switched JavaScript off (it is disabled). 2 An Introduction to Egyptian Mathematics Some of the oldest writing in the world is on a form of paper made from papyrus reeds that grew all along the Nile river in Egypt.
[The image is a link to David Joyce's site on the History of Maths at Clarke University.] So what was on them do you think? Continued Fractions - An introduction. Continued fractions are just another way of writing fractions.
They have some interesting connections with a jigsaw-puzzle problem about splitting a rectangle into squares and also with one of the oldest algorithms known to Greek mathematicians of 300 BC - Euclid's Algorithm - for computing the greatest divisor common to two numbers (gcd). An online Combined Continued Fraction Calculator is available in a separate window where you see Combined CF It is now updated to be a BigNumber Calculator that can handle very long whole numbers! (Jan 2018) An Introduction to Runsums. This page investigates numbers that are the sum of a run of whole numbers, such as 5+6+7 or 2+3+4+5+6, their properties and fascinating patterns.
Please note that this page now includes single numbers as runsums (they were excluded in versions of this page before Jan 2003). This makes formulae on later pages easier. A run of numbers is a sequence of consecutive whole numbers i.e. with no gaps in the sequence, Every number is therefore a sum of numbers in a run because we can have a run with just a single number in it! Many numbers can also be written as a sum of a run of 2 or more numbers. For convenience, the sum of a run of numbers we will call a runsum. Making a table of runsums Since every runsum is determined by its staring and ending number, we can make a table of the sums of integers between the two values: Exact Trig Values. Loading [MathJax]/jax/element/mml/optable/Latin1Supplement.js This page is about the trigonometric functions of sine, cosine and tangent, what they are and how to find the exact values of many angles.
The calculators and other effects on this page require JavaScript but you appear to have switched JavaScript off (it is disabled) in this browser. Please go to the Preferences or Properties menu item for this browser and enable it and then Reload this page. What angles have an exact expression for their sines, cosines and tangents? You might know that cos(60°)=1/2 and sin(60°)=√3/2 as well as tan(45°)=1, but are 30, 45 and 60 the only angles up to 90° with a formula for their trig values? 1 A Table of Exact Trig values that are expressible as simple terms involving square-roots. 2 All the trig functions in one diagram Here is a really great Mathematica demonstration of how all the 6 trigonometric functions are related, in one interactive diagram. 2.1 Trig functions of Angles <0° or >90° Phew! If. Pythagorean Triangles and Triples. The calculators on this page require JavaScript but you appear to have switched JavaScript off (it is disabled).
Please go to the Preferences for this browser and enable it if you want to use the calculators, then Reload this page. Right-angled triangles with whole number sides have fascinated mathematicians and number enthusiasts since well before 300 BC when Pythagoras wrote about his famous "theorem". The oldest mathematical document in the world, a little slab of clay that would fit in your hand, is a list of such triangles. So what is so fascinating about them? This page starts from scratch and has lots of facts and figures with several online calculators to help with your own investigations. 1 Right-angled Triangles and Pythagoras' Theorem 1.1 Pythagoras and Pythagoras' Theorem Pythagoras was a mathematician born in Greece in about 570 BC. For example, if the two shorter sides of a right-angled triangle are 2 cm and 3 cm, what is the length of the longest side? ) with sides a, b, c. Fibonacci Numbers, the Golden section and the Golden String.
Fibonacci Numbers and the Golden Section This is the Home page for Dr Ron Knott's multimedia web site on the Fibonacci numbers, the Golden section and the Golden string hosted by the Mathematics Department of the University of Surrey, UK.
The Fibonacci numbers are The golden section numbers are 0·61803 39887... = phi = φ and 1·61803 39887... = Phi = Φ The golden string is.