Summer Anne Burton over at Buzzfeed generated an awesome list of 24 Invaluable Skills to Learn for Free Online This Year, and numbers 1, 9, and 13 are especially dear to this mathematician's heart! Right now, I'm learning a new skill that's not as valuable: how to use a free Mac OS X utility called Grapher. Too bad it didn't exist back in the dark ages when I took Algebra II and Trigonometry!

Are you planning to learn any invaluable skills this year?

Yesterday, I paused the animation of inner planet orbit to record the dates of

Are you planning to learn any invaluable skills this year?

Yesterday, I paused the animation of inner planet orbit to record the dates of

**interior conjunction**of the sun, Venus, and Earth: August 15, 2015; March 26, 2017; October 22, 2018; June 13, 2020; and January 11, 2022. I noticed that Earth travels about a lap and a half in between each conjunction. The screenshot shows what I mean by interior conjunction (the sun, Venus, and Earth on the same line).A more exact way to put “about a lap and a half" is “eight years for every five conjunctions." That is eight-fifths, or 1.6. Fractions? Decimals? On the left is a picture to help you see that — a graphic I quickly created in a spreadsheet . When you make fifths pies with eight slices, you end up filling a whole pie (1) with five slices. So, you have to start a partial fifths pie and put three pieces in it (3/5). That is the fraction 1 and 3/5, or 8/5. And, if you run your finger around the curved edge of each pie, you end up going a lap and just over a half.

If you are a person who finds yourself “yet to know math,” ignore the fraction-decimal talk for now. Perhaps, that is a captain idea we can explore one day.

The pie chart makes me wonder where the point of conjunctions falls in the Earth's orbit, which I decided to label the orbits with the calculated date since my observed dates might be a little off. Using spreadsheets — number one on the list of 24 — becomes invaluable at the point.

How many days are there between each conjunction?

I multiplied 1.6 years by the number of days in a year (365.256) to get 584.41 days. Here is why spreadsheets are great if you dislike tedious calculations as much as I do. I can put the start date (1/11/2014) into a cell of the spreadsheet. In another cell, I can add 584.41 to the date and it tells me the new date. Then, I can copy that formula in the other cell to calculate all five conjunctions. Poof! Just like that! The spoilers page shows you my work.

If you are a person who finds yourself “yet to know math,” ignore the fraction-decimal talk for now. Perhaps, that is a captain idea we can explore one day.

The pie chart makes me wonder where the point of conjunctions falls in the Earth's orbit, which I decided to label the orbits with the calculated date since my observed dates might be a little off. Using spreadsheets — number one on the list of 24 — becomes invaluable at the point.

How many days are there between each conjunction?

I multiplied 1.6 years by the number of days in a year (365.256) to get 584.41 days. Here is why spreadsheets are great if you dislike tedious calculations as much as I do. I can put the start date (1/11/2014) into a cell of the spreadsheet. In another cell, I can add 584.41 to the date and it tells me the new date. Then, I can copy that formula in the other cell to calculate all five conjunctions. Poof! Just like that! The spoilers page shows you my work.

**Spreadsheets let you play with math without having to do the calculations!**In Grapher, the coolest thing happened as I plotted the interior conjunctions in order of time. As I put one conjunction after another, it automatically connected the dots for me ! The yellow circle in the middle is the sun; the orange orbit, Venus; and the blue, Earth. Connecting the conjunctions in order of time formed the brown star!

P.S. I never buy those homeschooling planners because I build my own using a spreadsheet. Tailored exactly to what I need!

P.S.S. 27 days and a wake-up until the winner of the potholder giveaway is announced. So, far, I have three names on the qualifying. What giveaway? Read on for more details.

P.S.S. 27 days and a wake-up until the winner of the potholder giveaway is announced. So, far, I have three names on the qualifying. What giveaway? Read on for more details.