Shooting to the moon (observational botany 4)

who: J2 and J1
where: dining room floor
when: Sunday morning

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Time for another update on our plants.

Orange Seeds
The bad news is that our orange seeds aren't making any progress.  Unknown to me, J1 had been putting the seeds out in the direct sun for several hours each day. This has possibly cooked the seeds. It is possible they weren't fertile in the first place. Of course, it is also possible they will still manage to sprout. We haven't tossed them out yet.

Avocado
The avocado has been a clear success. Since the last post, we hit the stage where the sprout was 6 inches long. This was the point our original instructions suggested we cut back to 3 inches. We were wondering why? After some searching on the internet, we concluded that most growers don't prune back at this stage and the purpose of doing so is to encourage a shorter, more bushy plant suitable for growing indoors. J1 and J2 were both keen to get the plant to grow as tall as possible (100 meters!) so we decided not to prune.

Some quick observations:

• J1: it is 25 cm tall
• J2: it has tertiary roots!
• J1 and J2: is that white stuff on the roots mold?

Ah well, even if it mold, the plant seems unaffected for now.


Root observation

We spent part of the morning sketching the roots. J1 was initially resistant, suggesting we should just work through technology ("why don't we just take a picture?") and that he had already drawn a picture of plant roots ("I already did that for school!") I explained that I was planning to draw the roots so I could practice close observation and asked if I could use his microscope. Telling him why I was going to do it seemed a very effective rhetorical strategy.

Here are our drawings:

AR1 by J1

AR1 By J2 (right) and J0 (left)

Avocado drama of the week
Our little baby is going touring this week! Well, actually just to school for one day, then back home the next.  Will it return intact?

Pseudosphere Hat and our Robot begins (some arts and crafts)

Who: J1
When: around lunchtime
where: on the floor

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Today, we tried making a couple of things. First up, was a pseudosphere.  The inspiration for this is a really nice post from Daniel Walsh: Sudo Make me a Pseudosphere. By all means go to the original post as the pictures, animations, and video he posted are far better than what we managed, but it was still a fun conversation about shapes, angles, slope, and fractions.

The process is easy:

1. cut out a bunch of equally sized circular discs
2. cut the discs into different sized (different angle) sectors
3. make all the pieces into cones
4. stack them from shallowest to steepest

Daniel mentioned something about calculating the optimal sizes, but I didn't really know what he meant. We went for a child's dinner plate for our circular template and cut sectors in multiples of 45 degrees.

Only the finest used newsprint for us!

One good question came up along the way: if I cut out a larger angle, will the cone we make be steeper or flatter?

Pseudosphere taking shape

There was another point where I'd cut out a 135 degree sector and J1 said: that's 1/3.  When he measured very roughly, it did seem to be a third, so I asked him to try it more precisely. He had a sudden realization when he saw the 90 degree remainder.

The cone of our dreams!

We went one step farther and permanently attached all the cones together, then re-purposed the whole thing to create 2015's fashion must-have item: the pseudo-rocket pseudosphere hat:

Starting our Robot

Our other activity is really the beginning of a longer project.. J1 has been talking about making a robot and we are starting to work on some of the main functions. Of course, he is really excited about camera eyes and a laser cannon, which we'll get to eventually (will we?) For now, I have some ideas about how to get the robot to walk.

My plan is to connect a basic rotating electric motor we have, so that leaves us solving an old problem: how to convert rotational motion into straight-line motion. Of course, wasteful methods are easy, but we want our robot to have the maximally powerful stride. For now, we are investigating multiple linkages, in the footsteps of Chebyshev.

Below is a first test: three linked arms:

1. Arm 1 has a fixed end and is intended to rotate in a circle
2. Arm 2 has one end fixed to the rotating end of arm 1. The other end of arm 2 is the motion we want to examine
3. Arm 3 has one end fixed and the other end attached to the mid-point of arm 2. This constrains that midpoint to travel along a circular arc

You can see our ultra-high tech implementation below, using card paper as the arms, a large cardboard box as the base, nails (into the base) to create fixed points, nails point up to create hinge joints, and extra bits of cardboard to cover the point ends of our hinges and past muster with  the health-and-safety inspectors:

The action of the multiple hinges is pretty wild. J1, J2, and I enjoyed cranking arm 1 and watching arm 2 fiddle around. Carefully holding a pencil in place, we managed to draw he path of arm 2's free end. It is the rounded wedge that looks very close to a circular quadrant.

If you want to see some great animations of multi-hinge contraptions, check out the animations at Mathematical Etudes. I'd be delighted if we could get close to this one.

Avocado update

I'm pleased to announce that another family member, D, has started sprouting her own avocado pit and, apparently, has made this into a race.  When told the news, J1 and J2 immediately started guessing what type of sabotage techniques would be employed by D. I think this says more about them than her.

Total mass: 67 grams
Length from root tip to sprout top: 21 cm
Length from pit to sprout top: 12.3 cm

Secondary Roots appear (observational botany 3)

Who: All J1 and J2
Where: at the dining table
When: after dinner (observations from 28 December/day 27)

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More progress on the avocado sprout. We had to transfer the pit as our previous glass bowl was too shallow and started to restrict the growth of the main root. Pictures courtesy of J1 this time.

Overview

Close-up of the split

Root view

Attention has drifted?

Observations
J1

• if we measure from outside the pit, the sprout is about 1 inch tall
• the sprout outside of the pit is light green with some red dots
• off of the main sprout, there are 6 tiny sprouts that look like little thorns, 4 above the pit and 2 inside
• there are also some black lines on the pit (J0 note: these are from where we cut the original avocado)
• the main root is flexible, the sprout only flexes a bit along the crack of the pit
• the secondary roots are more flexible than the main root.

J2

1. the avocado sprout looks like J1's nose (no one else agreed with this observation)
2. the part of the sprout inside the pit is white
3. the root has 5 pooplish (J0: what is this? J2: it is a little cm, daddy)
4. the toothpick are 5 peebolo (

Measurements:
the whole rig: 550 g
the rig less the pit: 486 g
from which we conclude that the pit plus 3 toothpicks: 64 g (unchanged from last measurement)

length of stem above the pit: 3.2cm (doesn't directly compare with our previous measurements)
length of main root below the pit: 2.9 cm (almost 1 cm longer than last time we measured)

Note: 3 days later on the 31st, the lengths were 6.5 cm above the pit and 14.5 cm total length. There was a striking and obvious growth spurt.

Sprouting! (observational botany 2)

Who: All Js
Where: at the dining table and in front of our house
When: after lunch (observations from 19 December/day 18)

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Avocado

Our avocado pit has made some progress.



J1's observations

• the root has sprouted
• maybe it is actually upside down and the avocado is confused?
• the pit split in the middle.
• there is a sprout in the middle
• some of the pit has peeled off
• the exposed pit is a bit more rough than when we examined it last week. it feels like bumpy wax.

J2's observations

1. Maybe it is actually upside down and the avocado is confused?
2. the avocado pit looks like it is going to poop on us (referring to the emerging root)
3. the exposed pit is smooth
4. the calculator is 9.5 cm long

J3's observations <made at dinner, had been napping while the older two discussed>

• There's a plant!
• These are floss, we use it to clean our teeth (gesturing to show how)
• Oh, some of the *this* fell off (noticing that dried skin from the pit was in the bottom of the water bowl from when one of the older two peeled it off and dropped it in).  

We also had a discussion about the division of the pit into two halves. When we started, there wasn't any clear indication that it would cleave along this line. We were wondering if there was some mechanism to prevent it from cleaving where we placed a toothpick, if the splitting location is random, or if there is a clear place it will split. I guess we add these to our curiosity list.

Measurements
3 toothpicks: 0 gr on our scale, indicating that they are less than 1/2 gram
The avocado pit and 3 toothpicks together was 64 grams (J2 noted this is 8 x 8)

The sprout in the middle of the pit and extending down was 4.5 cm long.
J0's nose is 6 cm long
J1's nose is 4.5 cm long, so the same as the sprout.
From end to end, the pit and root sprout are 7 cm.
The root protrusion is 2 cm.

When we started, we estimated the pit's mass 56 grams, (J2 remarks, 56 = 7.4833147 x 7.4833147)

J1 measured me with the tape measure and proclaimed that I have 101 kg of fat. His reasoning: some 

distance around was 101 cm and he assumed I must be 1 kg per cm of perimeter along that slice.

J2 added, the following.

√6 = 2.4494897

√4.5 = 2.1213203
I asked J2 if these square roots had any meaning, in the context of our seed. He said, "no, it is just for fun."

Introducing: Orange seeds

Last sunday (13 December) we planted some orange seeds. Vaguely following these instructions, we used two methods:

1. Planting in soil, keeping the soil covered and most: no developments yet
2. Planting in a pool of water with some soil and dried leaves: interesting developments this week

Our "interesting" case this week

So, what happened with the soaking seeds? Here are our observation notes:

• Oh, the seeds are sprouting!
• Hmm, the sprouts seem to be wiggling!
• Those aren't sprouts, they are larvae, probably mosquito larvae
• Ooh, it smells like cows. It stinks

We poured it out on the street in front of our house, in the sun, and watched the water dry out. We observed the larvae moving around in the small puddle of mud as it dried and talked about what they needed to survive. J2 noticed that there was a storm drain a meter away from the puddle and asked what would happen if they went down the drain. Then we talked about whether the could get to the drain (having to cross a meter of dry ground) and how they could know that there was a safe destination on the other side. We made conjectures about their senses and ability to communicate:

• probably cannot see/no eyes
• probably cannot talk, but we guess the do have a mouth to eat
• not sure about ears
• cannot read or write
• no ability to communicate with adult mosquitos, ants, humans, or other creatures

In summary, we concluded that their knowledge is restricted to the limited part of the universe that their limited senses can observe directly. Can you see the editorializing?

As you might expect, fire was introduced at some point in the conversation, we ended up burning a handful of dry leaves and some paper scraps. As you do, you know.

A christmas eve mystery

Who: J3
Where: at school
When: over 2 weeks

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This is actually something being done at school, but it matches our seed growing at home very nicely.
They did a couple of experiments to test the effect of different conditions on plant growth:

• with and without water
• in different potting media (soil, sand, rocks)
• with and without sunlight.

Here is the picture of the plants without (left) and with sunlight:

Sorry about the blur, this was my only shot through a swarm of excited toddlers

Thus, the mystery: why did the plants grown in the dark grow so much taller? Add your hypothesis in the comments!


This is a special day for our family: Grandpa G's birthday.  So, in the spirit of celebration and birthday wishes, we send some powers of 2 (and square relationships):

Sometimes 6s got to get a bit crazy, right?

Observational botany (step 1)

Who: All Js
Where: at the dining table (for future reference, this post has notes from 1 december 2014)
When: 5 minutes a day, before dinner

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The author of Five Triangles made a suggestion somewhere (maybe his/her other blog?) that a great science activity is to plant a seed and make observations of the developing plant for a year. We are starting this with an avocado pit.

The pencil is a stand-in until our dental hygiene
catches up to our scientific zeal

J1's observations

• The pencil smells like okra
• It's red gray
• It feels like my hair
• I think it is 5 cm long
• I estimate the mass is 1trn grams

J2's observations

• The avocado pit smells like okra
• It feels like your poop (J0:"My poop or your's?" "Your's daddy")
• It is 36 feet (J0:"Long, tall, or wide?" "Every dimension")
• It weighs 1000 pooplizes (J0: "what is 1 pooplize?" "The mass of all humans on the earth put together.")

As you can see, someone wasn't really taking this seriously

J3's observations

• This is floss (pointing) and this is floss (pointing again) and a pencil (pointing for a third time).
• It is not symmetrical
• One side is round and the other is pointy (indicating the side down in the water as round and the end pointing up as pointy)
• It is smooth
• it has no smell

J3 also asked for the pencil I was using to take notes, then drew some scribbles on the page and said she was drawing avocado pits.

Measurements
We made the following measures of mass:

• Empty bowl: 107 gr or 3 3/4 oz
• Pencil: 4 gr or 1/8 oz
• Dry pit+bowl+2 toothpicks+pencil: 167 gr or 5 7/8 oz
• water added: 133gr 

By implication, the pit and 2 toothpicks is 56 grams.

References:
A general procedure for growing your own avocado tree (don't expect to eat the fruit, though);
http://www.californiaavocado.com/grow-your-own-avocado-tree/

As usual, wikipedia has something useful to say (my emphasis added):

Usually, avocados are grown from pits indoors. This is often done by removing the pit from a ripe, unrefrigerated avocado. The pit is then stabbed with three or four toothpicks, about one-third of the way up. The pit is placed in a jar or vase containing tepid water. It should split in four to six weeks and yield roots and a sprout. If there is no change by this time, the avocado pit is discarded. Once the stem has grown a few inches, it is placed in a pot with soil. It should be watered every few days. Avocados have been known to grow large, so owners must be ready to repot the plant several times.

In other news
Doesn't the icosidodecahedron look oddly, asymmetrically misshapen?