It's a problem we must all have had. You desperately need to know the square root of a number, but the only available calculator doesn't have a square root button. How can you work it out? Of course, there are standard estimating techniques. Let's say we want to find the square root of 5. We … Continue reading Getting to the root of it
Category: Numbers
Fascinating facts about numbers – some from my own investigations and others unoriginal but interesting (to me at least)
153 as a number between squares
153 can be expressed as a2 + b2 and as (a+1)2 - (b+1)2. In other words, 122 + 32 = 153 = 132 - 42. This feature applies for every natural number b, with a equal to b2+b. So if b=4, this means a = 16 + 4 = 20. This gives 416 = 400 … Continue reading 153 as a number between squares
153 as the sum of factorials
The factorial of a number n (normally represented as n!) is found by multiplying together all the natural numbers up to n. So, for example, 4! = 1 x 2 x 3 x 4 = 24. 153 is the sum of the first five factorials: 1 + 2 + 6 + 24 + 120 = … Continue reading 153 as the sum of factorials
153 as a combination of squares
Take three square numbers and add them together. What numbers can you get? Potentially any whole number except one in the form 8n+7, 4 x (8m+7) 16 x (8l+7), 64 x (8k+7) etc. and many numbers can be formed by several different combinations. 153 is the first number that can be formed by combinations of … Continue reading 153 as a combination of squares
153 – a triangular number
A triangular number is one that can be represented by dots arranged in a triangle, where each row has one fewer dots than the one below it. The layout can be as a right-angled triangle, or as an equilateral one as illustrated on the left. Mathematically, the nth triangular number is the total of the … Continue reading 153 – a triangular number
153 – A narcissistic number
153 is a narcissistic number because 13 +53 +33 = 1 + 125 + 27 = 153. In general, a narcissistic number with k digits is one where the sum of raising each if its digits to the power k gives you the original number. So, for example, 84 + 24 + 04 + 84 … Continue reading 153 – A narcissistic number
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